%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG093+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:55:09 AM UTC 2026
% Result : Theorem 82.25s 82.55s
% Output : Proof 82.33s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mElmSort,axiom,
! [W0] :
( aElement0(W0)
=> $true ),
file('theBenchmark.p',mElmSort) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('theBenchmark.p',mSortsC) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('theBenchmark.p',mSortsC_01) ).
fof(mSortsU,axiom,
! [W0] :
( aElement0(W0)
=> aElement0(smndt0(W0)) ),
file('theBenchmark.p',mSortsU) ).
fof(mSortsB,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSortsB) ).
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mAddComm,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('theBenchmark.p',mAddComm) ).
fof(mAddAsso,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
file('theBenchmark.p',mAddAsso) ).
fof(mAddZero,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',mAddZero) ).
fof(mAddInvr,axiom,
! [W0] :
( aElement0(W0)
=> ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 ) ),
file('theBenchmark.p',mAddInvr) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('theBenchmark.p',mMulAsso) ).
fof(mMulUnit,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',mMulUnit) ).
fof(mAMDistr,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mAMDistr) ).
fof(mMulMnOne,axiom,
! [W0] :
( aElement0(W0)
=> ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),W0) = smndt0(W0) ) ),
file('theBenchmark.p',mMulMnOne) ).
fof(mMulZero,axiom,
! [W0] :
( aElement0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',mMulZero) ).
fof(mCancel,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W1 = sz00
| W0 = sz00 ) ) ),
file('theBenchmark.p',mCancel) ).
fof(mUnNeZr,axiom,
sz10 != sz00,
file('theBenchmark.p',mUnNeZr) ).
fof(mSetSort,axiom,
! [W0] :
( aSet0(W0)
=> $true ),
file('theBenchmark.p',mSetSort) ).
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mSetEq,axiom,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ( ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(W2,W1) ) )
=> W0 = W1 ) ),
file('theBenchmark.p',mSetEq) ).
fof(mDefSSum,definition,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSSum) ).
fof(mDefSInt,definition,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtasasdt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,W1)
& aElementOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSInt) ).
fof(mDefIdeal,definition,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('theBenchmark.p',mDefIdeal) ).
fof(mIdeSum,axiom,
! [W0,W1] :
( ( aIdeal0(W1)
& aIdeal0(W0) )
=> aIdeal0(sdtpldt1(W0,W1)) ),
file('theBenchmark.p',mIdeSum) ).
fof(m__1150,hypothesis,
( aIdeal0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) )
& ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('theBenchmark.p',m__1150) ).
fof(m__,conjecture,
( ( ! [W0] :
( aElementOf0(W0,sdtasasdt0(xI,xJ))
<=> ( aElementOf0(W0,xJ)
& aElementOf0(W0,xI) ) )
& aSet0(sdtasasdt0(xI,xJ)) )
=> ( aIdeal0(sdtasasdt0(xI,xJ))
| ! [W0] :
( aElementOf0(W0,sdtasasdt0(xI,xJ))
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),sdtasasdt0(xI,xJ)) )
& ! [W1] :
( aElementOf0(W1,sdtasasdt0(xI,xJ))
=> aElementOf0(sdtpldt0(W0,W1),sdtasasdt0(xI,xJ)) ) ) ) ) ),
file('theBenchmark.p',m__) ).
fof(f_1_1,plain,
! [W0] :
( $true
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mElmSort]) ).
fof(f_1_2,plain,
! [U_0] :
( $true
| ~ aElement0(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_0] : ~ aElement0(U_0)
| $true ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ aElement0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
aElement0(sz00),
inference(fof_nnf,[status(thm)],[mSortsC]) ).
cnf(f_2_2,plain,
aElement0(sz00),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
aElement0(sz10),
inference(fof_nnf,[status(thm)],[mSortsC_01]) ).
cnf(f_3_2,plain,
aElement0(sz10),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
! [W0] :
( aElement0(smndt0(W0))
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsU]) ).
fof(f_4_2,plain,
! [U_1] :
( aElement0(smndt0(U_1))
| ~ aElement0(U_1) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( aElement0(smndt0(U_1))
| ~ aElement0(U_1) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [W0,W1] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsB]) ).
fof(f_5_2,plain,
! [U_3,U_2] :
( aElement0(sdtpldt0(U_3,U_2))
| ~ aElement0(U_2)
| ~ aElement0(U_3) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( aElement0(sdtpldt0(U_3,U_2))
| ~ aElement0(U_2)
| ~ aElement0(U_3) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [W0,W1] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsB_02]) ).
fof(f_6_2,plain,
! [U_5,U_4] :
( aElement0(sdtasdt0(U_5,U_4))
| ~ aElement0(U_4)
| ~ aElement0(U_5) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( aElement0(sdtasdt0(U_5,U_4))
| ~ aElement0(U_4)
| ~ aElement0(U_5) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mAddComm]) ).
fof(f_7_2,plain,
! [U_7,U_6] :
( sdtpldt0(U_7,U_6) = sdtpldt0(U_6,U_7)
| ~ aElement0(U_6)
| ~ aElement0(U_7) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( sdtpldt0(U_7,U_6) = sdtpldt0(U_6,U_7)
| ~ aElement0(U_6)
| ~ aElement0(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [W0,W1,W2] :
( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2))
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mAddAsso]) ).
fof(f_8_2,plain,
! [U_10,U_9,U_8] :
( sdtpldt0(sdtpldt0(U_10,U_9),U_8) = sdtpldt0(U_10,sdtpldt0(U_9,U_8))
| ~ aElement0(U_8)
| ~ aElement0(U_9)
| ~ aElement0(U_10) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( sdtpldt0(sdtpldt0(U_10,U_9),U_8) = sdtpldt0(U_10,sdtpldt0(U_9,U_8))
| ~ aElement0(U_8)
| ~ aElement0(U_9)
| ~ aElement0(U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mAddZero]) ).
fof(f_9_2,plain,
! [U_11] :
( ( U_11 = sdtpldt0(sz00,U_11)
& sdtpldt0(U_11,sz00) = U_11 )
| ~ aElement0(U_11) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( sdtpldt0(U_11,sz00) = U_11
| ~ aElement0(U_11) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( U_11 = sdtpldt0(sz00,U_11)
| ~ aElement0(U_11) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [W0] :
( ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mAddInvr]) ).
fof(f_10_2,plain,
! [U_12] :
( ( sz00 = sdtpldt0(smndt0(U_12),U_12)
& sdtpldt0(U_12,smndt0(U_12)) = sz00 )
| ~ aElement0(U_12) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( sdtpldt0(U_12,smndt0(U_12)) = sz00
| ~ aElement0(U_12) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( sz00 = sdtpldt0(smndt0(U_12),U_12)
| ~ aElement0(U_12) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mMulComm]) ).
fof(f_11_2,plain,
! [U_14,U_13] :
( sdtasdt0(U_14,U_13) = sdtasdt0(U_13,U_14)
| ~ aElement0(U_13)
| ~ aElement0(U_14) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( sdtasdt0(U_14,U_13) = sdtasdt0(U_13,U_14)
| ~ aElement0(U_13)
| ~ aElement0(U_14) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mMulAsso]) ).
fof(f_12_2,plain,
! [U_17,U_16,U_15] :
( sdtasdt0(sdtasdt0(U_17,U_16),U_15) = sdtasdt0(U_17,sdtasdt0(U_16,U_15))
| ~ aElement0(U_15)
| ~ aElement0(U_16)
| ~ aElement0(U_17) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( sdtasdt0(sdtasdt0(U_17,U_16),U_15) = sdtasdt0(U_17,sdtasdt0(U_16,U_15))
| ~ aElement0(U_15)
| ~ aElement0(U_16)
| ~ aElement0(U_17) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mMulUnit]) ).
fof(f_13_2,plain,
! [U_18] :
( ( U_18 = sdtasdt0(sz10,U_18)
& sdtasdt0(U_18,sz10) = U_18 )
| ~ aElement0(U_18) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( sdtasdt0(U_18,sz10) = U_18
| ~ aElement0(U_18) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( U_18 = sdtasdt0(sz10,U_18)
| ~ aElement0(U_18) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mAMDistr]) ).
fof(f_14_2,plain,
! [U_21,U_20,U_19] :
( ( sdtasdt0(sdtpldt0(U_20,U_19),U_21) = sdtpldt0(sdtasdt0(U_20,U_21),sdtasdt0(U_19,U_21))
& sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19)) )
| ~ aElement0(U_19)
| ~ aElement0(U_20)
| ~ aElement0(U_21) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( sdtasdt0(U_21,sdtpldt0(U_20,U_19)) = sdtpldt0(sdtasdt0(U_21,U_20),sdtasdt0(U_21,U_19))
| ~ aElement0(U_19)
| ~ aElement0(U_20)
| ~ aElement0(U_21) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( sdtasdt0(sdtpldt0(U_20,U_19),U_21) = sdtpldt0(sdtasdt0(U_20,U_21),sdtasdt0(U_19,U_21))
| ~ aElement0(U_19)
| ~ aElement0(U_20)
| ~ aElement0(U_21) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [W0] :
( ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mMulMnOne]) ).
fof(f_15_2,plain,
! [U_22] :
( ( smndt0(U_22) = sdtasdt0(U_22,smndt0(sz10))
& sdtasdt0(smndt0(sz10),U_22) = smndt0(U_22) )
| ~ aElement0(U_22) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( sdtasdt0(smndt0(sz10),U_22) = smndt0(U_22)
| ~ aElement0(U_22) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( smndt0(U_22) = sdtasdt0(U_22,smndt0(sz10))
| ~ aElement0(U_22) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mMulZero]) ).
fof(f_16_2,plain,
! [U_23] :
( ( sz00 = sdtasdt0(sz00,U_23)
& sdtasdt0(U_23,sz00) = sz00 )
| ~ aElement0(U_23) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( sdtasdt0(U_23,sz00) = sz00
| ~ aElement0(U_23) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( sz00 = sdtasdt0(sz00,U_23)
| ~ aElement0(U_23) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [W0,W1] :
( W1 = sz00
| W0 = sz00
| sdtasdt0(W0,W1) != sz00
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mCancel]) ).
fof(f_17_2,plain,
! [U_25,U_24] :
( U_24 = sz00
| U_25 = sz00
| sdtasdt0(U_25,U_24) != sz00
| ~ aElement0(U_24)
| ~ aElement0(U_25) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( U_24 = sz00
| U_25 = sz00
| sdtasdt0(U_25,U_24) != sz00
| ~ aElement0(U_24)
| ~ aElement0(U_25) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
sz10 != sz00,
inference(fof_nnf,[status(thm)],[mUnNeZr]) ).
cnf(f_18_2,plain,
sz10 != sz00,
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
! [W0] :
( $true
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSetSort]) ).
fof(f_19_2,plain,
! [U_26] :
( $true
| ~ aSet0(U_26) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_26] : ~ aSet0(U_26)
| $true ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( ~ aSet0(U_26)
| $true ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mEOfElem]) ).
fof(f_20_2,plain,
! [U_28] :
( ! [U_27] :
( aElement0(U_27)
| ~ aElementOf0(U_27,U_28) )
| ~ aSet0(U_28) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( aElement0(U_27)
| ~ aElementOf0(U_27,U_28)
| ~ aSet0(U_28) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [W0,W1] :
( W0 = W1
| ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ? [W2] :
( ~ aElementOf0(W2,W1)
& aElementOf0(W2,W0) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSetEq]) ).
fof(f_21_2,plain,
! [U_32,U_31] :
( U_32 = U_31
| ? [U_30] :
( ~ aElementOf0(U_30,U_32)
& aElementOf0(U_30,U_31) )
| ? [U_29] :
( ~ aElementOf0(U_29,U_31)
& aElementOf0(U_29,U_32) )
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_32,U_31] :
( U_32 = U_31
| ? [U_30] :
( ~ aElementOf0(U_30,U_32)
& aElementOf0(U_30,U_31) )
| ( ~ aElementOf0(sK1(U_32,U_31),U_31)
& aElementOf0(sK1(U_32,U_31),U_32) )
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_29,sK1(U_32,U_31))],[f_21_2]) ).
fof(f_21_4,plain,
! [U_32,U_31] :
( U_32 = U_31
| ( ~ aElementOf0(sK2(U_32,U_31),U_32)
& aElementOf0(sK2(U_32,U_31),U_31) )
| ( ~ aElementOf0(sK1(U_32,U_31),U_31)
& aElementOf0(sK1(U_32,U_31),U_32) )
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_30,sK2(U_32,U_31))],[f_21_3]) ).
cnf(f_21_5,plain,
( aElementOf0(sK2(U_32,U_31),U_31)
| aElementOf0(sK1(U_32,U_31),U_32)
| U_32 = U_31
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_6,plain,
( ~ aElementOf0(sK2(U_32,U_31),U_32)
| aElementOf0(sK1(U_32,U_31),U_32)
| U_32 = U_31
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_7,plain,
( aElementOf0(sK2(U_32,U_31),U_31)
| ~ aElementOf0(sK1(U_32,U_31),U_31)
| U_32 = U_31
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_8,plain,
( ~ aElementOf0(sK2(U_32,U_31),U_32)
| ~ aElementOf0(sK1(U_32,U_31),U_31)
| U_32 = U_31
| ~ aSet0(U_31)
| ~ aSet0(U_32) ),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtpldt1(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
| ( ! [W4,W5] :
( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| ! [W4,W5] :
( sdtpldt0(W4,W5) != W3
| ~ aElementOf0(W5,W1)
| ~ aElementOf0(W4,W0) ) )
& ( ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSSum]) ).
fof(f_22_2,plain,
! [U_45,U_44] :
( ! [U_43] :
( ( U_43 = sdtpldt1(U_45,U_44)
| ? [U_42] :
( ( ~ aElementOf0(U_42,U_43)
& ? [U_41,U_40] :
( sdtpldt0(U_41,U_40) = U_42
& aElementOf0(U_40,U_44)
& aElementOf0(U_41,U_45) ) )
| ( ! [U_39,U_38] :
( sdtpldt0(U_39,U_38) != U_42
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(U_42,U_43) ) )
| ~ aSet0(U_43) )
& ( ( ! [U_37] :
( ( aElementOf0(U_37,U_43)
| ! [U_36,U_35] :
( sdtpldt0(U_36,U_35) != U_37
| ~ aElementOf0(U_35,U_44)
| ~ aElementOf0(U_36,U_45) ) )
& ( ? [U_34,U_33] :
( sdtpldt0(U_34,U_33) = U_37
& aElementOf0(U_33,U_44)
& aElementOf0(U_34,U_45) )
| ~ aElementOf0(U_37,U_43) ) )
& aSet0(U_43) )
| U_43 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ? [U_49] :
( ~ aElementOf0(U_49,U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = U_49
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ? [U_48] :
( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != U_48
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(U_48,U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ? [U_34] :
( ? [U_33] :
( sdtpldt0(U_34,U_33) = U_46
& aElementOf0(U_33,U_44) )
& aElementOf0(U_34,U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ? [U_49] :
( ~ aElementOf0(U_49,U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = U_49
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ? [U_48] :
( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != U_48
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(U_48,U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( ? [U_33] :
( sdtpldt0(sK3(U_45,U_44,U_50,U_46),U_33) = U_46
& aElementOf0(U_33,U_44) )
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_34,sK3(U_45,U_44,U_50,U_46))],[f_22_3]) ).
fof(f_22_5,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ? [U_49] :
( ~ aElementOf0(U_49,U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = U_49
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ? [U_48] :
( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != U_48
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(U_48,U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_33,sK4(U_45,U_44,U_50,U_46))],[f_22_4]) ).
fof(f_22_6,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ? [U_49] :
( ~ aElementOf0(U_49,U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = U_49
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(sK5(U_45,U_44,U_51),U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_48,sK5(U_45,U_44,U_51))],[f_22_5]) ).
fof(f_22_7,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
& ? [U_41] :
( ? [U_40] :
( sdtpldt0(U_41,U_40) = sK6(U_45,U_44,U_51)
& aElementOf0(U_40,U_44) )
& aElementOf0(U_41,U_45) ) )
| ( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(sK5(U_45,U_44,U_51),U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_49,sK6(U_45,U_44,U_51))],[f_22_6]) ).
fof(f_22_8,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
& ? [U_40] :
( sdtpldt0(sK7(U_45,U_44,U_51),U_40) = sK6(U_45,U_44,U_51)
& aElementOf0(U_40,U_44) )
& aElementOf0(sK7(U_45,U_44,U_51),U_45) )
| ( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(sK5(U_45,U_44,U_51),U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_41,sK7(U_45,U_44,U_51))],[f_22_7]) ).
fof(f_22_9,plain,
! [U_45,U_44] :
( ( ! [U_51] :
( U_51 = sdtpldt1(U_45,U_44)
| ( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
& sdtpldt0(sK7(U_45,U_44,U_51),sK8(U_45,U_44,U_51)) = sK6(U_45,U_44,U_51)
& aElementOf0(sK8(U_45,U_44,U_51),U_44)
& aElementOf0(sK7(U_45,U_44,U_51),U_45) )
| ( ! [U_39] :
( ! [U_38] :
( sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44) )
| ~ aElementOf0(U_39,U_45) )
& aElementOf0(sK5(U_45,U_44,U_51),U_51) )
| ~ aSet0(U_51) )
& ! [U_50] :
( ( ! [U_47] :
( aElementOf0(U_47,U_50)
| ! [U_36] :
( ! [U_35] :
( sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44) )
| ~ aElementOf0(U_36,U_45) ) )
& ! [U_46] :
( ( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
& aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
& aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45) )
| ~ aElementOf0(U_46,U_50) )
& aSet0(U_50) )
| U_50 != sdtpldt1(U_45,U_44) ) )
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_40,sK8(U_45,U_44,U_51))],[f_22_8]) ).
cnf(f_22_10,plain,
( aSet0(U_50)
| U_50 != sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_11,plain,
( aElementOf0(sK3(U_45,U_44,U_50,U_46),U_45)
| ~ aElementOf0(U_46,U_50)
| U_50 != sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_12,plain,
( aElementOf0(sK4(U_45,U_44,U_50,U_46),U_44)
| ~ aElementOf0(U_46,U_50)
| U_50 != sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_13,plain,
( sdtpldt0(sK3(U_45,U_44,U_50,U_46),sK4(U_45,U_44,U_50,U_46)) = U_46
| ~ aElementOf0(U_46,U_50)
| U_50 != sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_14,plain,
( aElementOf0(U_47,U_50)
| sdtpldt0(U_36,U_35) != U_47
| ~ aElementOf0(U_35,U_44)
| ~ aElementOf0(U_36,U_45)
| U_50 != sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_15,plain,
( aElementOf0(sK7(U_45,U_44,U_51),U_45)
| aElementOf0(sK5(U_45,U_44,U_51),U_51)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_16,plain,
( aElementOf0(sK8(U_45,U_44,U_51),U_44)
| aElementOf0(sK5(U_45,U_44,U_51),U_51)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_17,plain,
( sdtpldt0(sK7(U_45,U_44,U_51),sK8(U_45,U_44,U_51)) = sK6(U_45,U_44,U_51)
| aElementOf0(sK5(U_45,U_44,U_51),U_51)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_18,plain,
( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
| aElementOf0(sK5(U_45,U_44,U_51),U_51)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_19,plain,
( aElementOf0(sK7(U_45,U_44,U_51),U_45)
| sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_20,plain,
( aElementOf0(sK8(U_45,U_44,U_51),U_44)
| sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_21,plain,
( sdtpldt0(sK7(U_45,U_44,U_51),sK8(U_45,U_44,U_51)) = sK6(U_45,U_44,U_51)
| sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_22,plain,
( ~ aElementOf0(sK6(U_45,U_44,U_51),U_51)
| sdtpldt0(U_39,U_38) != sK5(U_45,U_44,U_51)
| ~ aElementOf0(U_38,U_44)
| ~ aElementOf0(U_39,U_45)
| ~ aSet0(U_51)
| U_51 = sdtpldt1(U_45,U_44)
| ~ aSet0(U_44)
| ~ aSet0(U_45) ),
inference(clausify,[status(thm)],[f_22_9]) ).
fof(f_23_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtasasdt0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& aElementOf0(W3,W1)
& aElementOf0(W3,W0) )
| ( ( ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| ~ aElementOf0(W3,W1)
| ~ aElementOf0(W3,W0) )
& ( ( aElementOf0(W3,W1)
& aElementOf0(W3,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtasasdt0(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSInt]) ).
fof(f_23_2,plain,
! [U_56,U_55] :
( ! [U_54] :
( ( U_54 = sdtasasdt0(U_56,U_55)
| ? [U_53] :
( ( ~ aElementOf0(U_53,U_54)
& aElementOf0(U_53,U_55)
& aElementOf0(U_53,U_56) )
| ( ( ~ aElementOf0(U_53,U_55)
| ~ aElementOf0(U_53,U_56) )
& aElementOf0(U_53,U_54) ) )
| ~ aSet0(U_54) )
& ( ( ! [U_52] :
( ( aElementOf0(U_52,U_54)
| ~ aElementOf0(U_52,U_55)
| ~ aElementOf0(U_52,U_56) )
& ( ( aElementOf0(U_52,U_55)
& aElementOf0(U_52,U_56) )
| ~ aElementOf0(U_52,U_54) ) )
& aSet0(U_54) )
| U_54 != sdtasasdt0(U_56,U_55) ) )
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_56,U_55] :
( ( ! [U_62] :
( U_62 = sdtasasdt0(U_56,U_55)
| ? [U_60] :
( ~ aElementOf0(U_60,U_62)
& aElementOf0(U_60,U_55)
& aElementOf0(U_60,U_56) )
| ? [U_59] :
( ( ~ aElementOf0(U_59,U_55)
| ~ aElementOf0(U_59,U_56) )
& aElementOf0(U_59,U_62) )
| ~ aSet0(U_62) )
& ! [U_61] :
( ( ! [U_58] :
( aElementOf0(U_58,U_61)
| ~ aElementOf0(U_58,U_55)
| ~ aElementOf0(U_58,U_56) )
& ! [U_57] :
( ( aElementOf0(U_57,U_55)
& aElementOf0(U_57,U_56) )
| ~ aElementOf0(U_57,U_61) )
& aSet0(U_61) )
| U_61 != sdtasasdt0(U_56,U_55) ) )
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
! [U_56,U_55] :
( ( ! [U_62] :
( U_62 = sdtasasdt0(U_56,U_55)
| ? [U_60] :
( ~ aElementOf0(U_60,U_62)
& aElementOf0(U_60,U_55)
& aElementOf0(U_60,U_56) )
| ( ( ~ aElementOf0(sK9(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_56) )
& aElementOf0(sK9(U_56,U_55,U_62),U_62) )
| ~ aSet0(U_62) )
& ! [U_61] :
( ( ! [U_58] :
( aElementOf0(U_58,U_61)
| ~ aElementOf0(U_58,U_55)
| ~ aElementOf0(U_58,U_56) )
& ! [U_57] :
( ( aElementOf0(U_57,U_55)
& aElementOf0(U_57,U_56) )
| ~ aElementOf0(U_57,U_61) )
& aSet0(U_61) )
| U_61 != sdtasasdt0(U_56,U_55) ) )
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_59,sK9(U_56,U_55,U_62))],[f_23_3]) ).
fof(f_23_5,plain,
! [U_56,U_55] :
( ( ! [U_62] :
( U_62 = sdtasasdt0(U_56,U_55)
| ( ~ aElementOf0(sK10(U_56,U_55,U_62),U_62)
& aElementOf0(sK10(U_56,U_55,U_62),U_55)
& aElementOf0(sK10(U_56,U_55,U_62),U_56) )
| ( ( ~ aElementOf0(sK9(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_56) )
& aElementOf0(sK9(U_56,U_55,U_62),U_62) )
| ~ aSet0(U_62) )
& ! [U_61] :
( ( ! [U_58] :
( aElementOf0(U_58,U_61)
| ~ aElementOf0(U_58,U_55)
| ~ aElementOf0(U_58,U_56) )
& ! [U_57] :
( ( aElementOf0(U_57,U_55)
& aElementOf0(U_57,U_56) )
| ~ aElementOf0(U_57,U_61) )
& aSet0(U_61) )
| U_61 != sdtasasdt0(U_56,U_55) ) )
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_60,sK10(U_56,U_55,U_62))],[f_23_4]) ).
cnf(f_23_6,plain,
( aSet0(U_61)
| U_61 != sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_7,plain,
( aElementOf0(U_57,U_56)
| ~ aElementOf0(U_57,U_61)
| U_61 != sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_8,plain,
( aElementOf0(U_57,U_55)
| ~ aElementOf0(U_57,U_61)
| U_61 != sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_9,plain,
( aElementOf0(U_58,U_61)
| ~ aElementOf0(U_58,U_55)
| ~ aElementOf0(U_58,U_56)
| U_61 != sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_10,plain,
( aElementOf0(sK10(U_56,U_55,U_62),U_56)
| aElementOf0(sK9(U_56,U_55,U_62),U_62)
| ~ aSet0(U_62)
| U_62 = sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_11,plain,
( aElementOf0(sK10(U_56,U_55,U_62),U_55)
| aElementOf0(sK9(U_56,U_55,U_62),U_62)
| ~ aSet0(U_62)
| U_62 = sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_12,plain,
( ~ aElementOf0(sK10(U_56,U_55,U_62),U_62)
| aElementOf0(sK9(U_56,U_55,U_62),U_62)
| ~ aSet0(U_62)
| U_62 = sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_13,plain,
( aElementOf0(sK10(U_56,U_55,U_62),U_56)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_56)
| ~ aSet0(U_62)
| U_62 = sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_14,plain,
( aElementOf0(sK10(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_56)
| ~ aSet0(U_62)
| U_62 = sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_15,plain,
( ~ aElementOf0(sK10(U_56,U_55,U_62),U_62)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_55)
| ~ aElementOf0(sK9(U_56,U_55,U_62),U_56)
| ~ aSet0(U_62)
| U_62 = sdtasasdt0(U_56,U_55)
| ~ aSet0(U_55)
| ~ aSet0(U_56) ),
inference(clausify,[status(thm)],[f_23_5]) ).
fof(f_24_1,plain,
! [W0] :
( ( aIdeal0(W0)
| ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0) )
& ( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(fof_nnf,[status(thm)],[mDefIdeal]) ).
fof(f_24_2,plain,
! [U_69] :
( ( aIdeal0(U_69)
| ? [U_68] :
( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,U_68),U_69)
& aElement0(U_67) )
| ? [U_66] :
( ~ aElementOf0(sdtpldt0(U_68,U_66),U_69)
& aElementOf0(U_66,U_69) ) )
& aElementOf0(U_68,U_69) )
| ~ aSet0(U_69) )
& ( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_69)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_69)
| ~ aElementOf0(U_63,U_69) ) )
| ~ aElementOf0(U_65,U_69) )
& aSet0(U_69) )
| ~ aIdeal0(U_69) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ? [U_68] :
( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,U_68),U_71)
& aElement0(U_67) )
| ? [U_66] :
( ~ aElementOf0(sdtpldt0(U_68,U_66),U_71)
& aElementOf0(U_66,U_71) ) )
& aElementOf0(U_68,U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,sK11(U_71)),U_71)
& aElement0(U_67) )
| ? [U_66] :
( ~ aElementOf0(sdtpldt0(sK11(U_71),U_66),U_71)
& aElementOf0(U_66,U_71) ) )
& aElementOf0(sK11(U_71),U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_68,sK11(U_71))],[f_24_3]) ).
fof(f_24_5,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,sK11(U_71)),U_71)
& aElement0(U_67) )
| ( ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
& aElementOf0(sK12(U_71),U_71) ) )
& aElementOf0(sK11(U_71),U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_66,sK12(U_71))],[f_24_4]) ).
fof(f_24_6,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ( ( ( ~ aElementOf0(sdtasdt0(sK13(U_71),sK11(U_71)),U_71)
& aElement0(sK13(U_71)) )
| ( ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
& aElementOf0(sK12(U_71),U_71) ) )
& aElementOf0(sK11(U_71),U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_67,sK13(U_71))],[f_24_5]) ).
cnf(f_24_7,plain,
( aSet0(U_70)
| ~ aIdeal0(U_70) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_8,plain,
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70)
| ~ aElementOf0(U_65,U_70)
| ~ aIdeal0(U_70) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_9,plain,
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64)
| ~ aElementOf0(U_65,U_70)
| ~ aIdeal0(U_70) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_10,plain,
( aElementOf0(sK11(U_71),U_71)
| ~ aSet0(U_71)
| aIdeal0(U_71) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_11,plain,
( aElement0(sK13(U_71))
| aElementOf0(sK12(U_71),U_71)
| ~ aSet0(U_71)
| aIdeal0(U_71) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_12,plain,
( ~ aElementOf0(sdtasdt0(sK13(U_71),sK11(U_71)),U_71)
| aElementOf0(sK12(U_71),U_71)
| ~ aSet0(U_71)
| aIdeal0(U_71) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_13,plain,
( aElement0(sK13(U_71))
| ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
| ~ aSet0(U_71)
| aIdeal0(U_71) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_14,plain,
( ~ aElementOf0(sdtasdt0(sK13(U_71),sK11(U_71)),U_71)
| ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
| ~ aSet0(U_71)
| aIdeal0(U_71) ),
inference(clausify,[status(thm)],[f_24_6]) ).
fof(f_25_1,plain,
! [W0,W1] :
( aIdeal0(sdtpldt1(W0,W1))
| ~ aIdeal0(W1)
| ~ aIdeal0(W0) ),
inference(fof_nnf,[status(thm)],[mIdeSum]) ).
fof(f_25_2,plain,
! [U_73,U_72] :
( aIdeal0(sdtpldt1(U_73,U_72))
| ~ aIdeal0(U_72)
| ~ aIdeal0(U_73) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( aIdeal0(sdtpldt1(U_73,U_72))
| ~ aIdeal0(U_72)
| ~ aIdeal0(U_73) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
( aIdeal0(xJ)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xJ)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xJ)
| ~ aElementOf0(W1,xJ) ) )
| ~ aElementOf0(W0,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(fof_nnf,[status(thm)],[m__1150]) ).
fof(f_26_2,plain,
( aIdeal0(xJ)
& ! [U_79] :
( ( ! [U_78] :
( aElementOf0(sdtasdt0(U_78,U_79),xJ)
| ~ aElement0(U_78) )
& ! [U_77] :
( aElementOf0(sdtpldt0(U_79,U_77),xJ)
| ~ aElementOf0(U_77,xJ) ) )
| ~ aElementOf0(U_79,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [U_76] :
( ( ! [U_75] :
( aElementOf0(sdtasdt0(U_75,U_76),xI)
| ~ aElement0(U_75) )
& ! [U_74] :
( aElementOf0(sdtpldt0(U_76,U_74),xI)
| ~ aElementOf0(U_74,xI) ) )
| ~ aElementOf0(U_76,xI) )
& aSet0(xI) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
aSet0(xI),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( aElementOf0(sdtpldt0(U_76,U_74),xI)
| ~ aElementOf0(U_74,xI)
| ~ aElementOf0(U_76,xI) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_5,plain,
( aElementOf0(sdtasdt0(U_75,U_76),xI)
| ~ aElement0(U_75)
| ~ aElementOf0(U_76,xI) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_6,plain,
aIdeal0(xI),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_7,plain,
aSet0(xJ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_8,plain,
( aElementOf0(sdtpldt0(U_79,U_77),xJ)
| ~ aElementOf0(U_77,xJ)
| ~ aElementOf0(U_79,xJ) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_9,plain,
( aElementOf0(sdtasdt0(U_78,U_79),xJ)
| ~ aElement0(U_78)
| ~ aElementOf0(U_79,xJ) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_10,plain,
aIdeal0(xJ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,negated_conjecture,
( ~ ( aIdeal0(sdtasasdt0(xI,xJ))
| ! [W0] :
( aElementOf0(W0,sdtasasdt0(xI,xJ))
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),sdtasasdt0(xI,xJ)) )
& ! [W1] :
( aElementOf0(W1,sdtasasdt0(xI,xJ))
=> aElementOf0(sdtpldt0(W0,W1),sdtasasdt0(xI,xJ)) ) ) ) )
& ! [W0] :
( aElementOf0(W0,sdtasasdt0(xI,xJ))
<=> ( aElementOf0(W0,xJ)
& aElementOf0(W0,xI) ) )
& aSet0(sdtasasdt0(xI,xJ)) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_27_2,negated_conjecture,
( ~ aIdeal0(sdtasasdt0(xI,xJ))
& ? [W0] :
( ( ? [W1] :
( ~ aElementOf0(sdtasdt0(W1,W0),sdtasasdt0(xI,xJ))
& aElement0(W1) )
| ? [W1] :
( ~ aElementOf0(sdtpldt0(W0,W1),sdtasasdt0(xI,xJ))
& aElementOf0(W1,sdtasasdt0(xI,xJ)) ) )
& aElementOf0(W0,sdtasasdt0(xI,xJ)) )
& ! [W0] :
( ( aElementOf0(W0,sdtasasdt0(xI,xJ))
| ~ aElementOf0(W0,xJ)
| ~ aElementOf0(W0,xI) )
& ( ( aElementOf0(W0,xJ)
& aElementOf0(W0,xI) )
| ~ aElementOf0(W0,sdtasasdt0(xI,xJ)) ) )
& aSet0(sdtasasdt0(xI,xJ)) ),
inference(fof_nnf,[status(thm)],[f_27_1]) ).
fof(f_27_3,negated_conjecture,
( ~ aIdeal0(sdtasasdt0(xI,xJ))
& ? [U_83] :
( ( ? [U_82] :
( ~ aElementOf0(sdtasdt0(U_82,U_83),sdtasasdt0(xI,xJ))
& aElement0(U_82) )
| ? [U_81] :
( ~ aElementOf0(sdtpldt0(U_83,U_81),sdtasasdt0(xI,xJ))
& aElementOf0(U_81,sdtasasdt0(xI,xJ)) ) )
& aElementOf0(U_83,sdtasasdt0(xI,xJ)) )
& ! [U_80] :
( ( aElementOf0(U_80,sdtasasdt0(xI,xJ))
| ~ aElementOf0(U_80,xJ)
| ~ aElementOf0(U_80,xI) )
& ( ( aElementOf0(U_80,xJ)
& aElementOf0(U_80,xI) )
| ~ aElementOf0(U_80,sdtasasdt0(xI,xJ)) ) )
& aSet0(sdtasasdt0(xI,xJ)) ),
inference(variable_rename,[status(thm)],[f_27_2]) ).
fof(f_27_4,negated_conjecture,
( ~ aIdeal0(sdtasasdt0(xI,xJ))
& ? [U_83] :
( ( ? [U_82] :
( ~ aElementOf0(sdtasdt0(U_82,U_83),sdtasasdt0(xI,xJ))
& aElement0(U_82) )
| ? [U_81] :
( ~ aElementOf0(sdtpldt0(U_83,U_81),sdtasasdt0(xI,xJ))
& aElementOf0(U_81,sdtasasdt0(xI,xJ)) ) )
& aElementOf0(U_83,sdtasasdt0(xI,xJ)) )
& ! [U_85] :
( aElementOf0(U_85,sdtasasdt0(xI,xJ))
| ~ aElementOf0(U_85,xJ)
| ~ aElementOf0(U_85,xI) )
& ! [U_84] :
( ( aElementOf0(U_84,xJ)
& aElementOf0(U_84,xI) )
| ~ aElementOf0(U_84,sdtasasdt0(xI,xJ)) )
& aSet0(sdtasasdt0(xI,xJ)) ),
inference(miniscope,[status(thm)],[f_27_3]) ).
fof(f_27_5,negated_conjecture,
( ~ aIdeal0(sdtasasdt0(xI,xJ))
& ( ? [U_82] :
( ~ aElementOf0(sdtasdt0(U_82,sK14),sdtasasdt0(xI,xJ))
& aElement0(U_82) )
| ? [U_81] :
( ~ aElementOf0(sdtpldt0(sK14,U_81),sdtasasdt0(xI,xJ))
& aElementOf0(U_81,sdtasasdt0(xI,xJ)) ) )
& aElementOf0(sK14,sdtasasdt0(xI,xJ))
& ! [U_85] :
( aElementOf0(U_85,sdtasasdt0(xI,xJ))
| ~ aElementOf0(U_85,xJ)
| ~ aElementOf0(U_85,xI) )
& ! [U_84] :
( ( aElementOf0(U_84,xJ)
& aElementOf0(U_84,xI) )
| ~ aElementOf0(U_84,sdtasasdt0(xI,xJ)) )
& aSet0(sdtasasdt0(xI,xJ)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_83,sK14)],[f_27_4]) ).
fof(f_27_6,negated_conjecture,
( ~ aIdeal0(sdtasasdt0(xI,xJ))
& ( ? [U_82] :
( ~ aElementOf0(sdtasdt0(U_82,sK14),sdtasasdt0(xI,xJ))
& aElement0(U_82) )
| ( ~ aElementOf0(sdtpldt0(sK14,sK15),sdtasasdt0(xI,xJ))
& aElementOf0(sK15,sdtasasdt0(xI,xJ)) ) )
& aElementOf0(sK14,sdtasasdt0(xI,xJ))
& ! [U_85] :
( aElementOf0(U_85,sdtasasdt0(xI,xJ))
| ~ aElementOf0(U_85,xJ)
| ~ aElementOf0(U_85,xI) )
& ! [U_84] :
( ( aElementOf0(U_84,xJ)
& aElementOf0(U_84,xI) )
| ~ aElementOf0(U_84,sdtasasdt0(xI,xJ)) )
& aSet0(sdtasasdt0(xI,xJ)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_81,sK15)],[f_27_5]) ).
fof(f_27_7,negated_conjecture,
( ~ aIdeal0(sdtasasdt0(xI,xJ))
& ( ( ~ aElementOf0(sdtasdt0(sK16,sK14),sdtasasdt0(xI,xJ))
& aElement0(sK16) )
| ( ~ aElementOf0(sdtpldt0(sK14,sK15),sdtasasdt0(xI,xJ))
& aElementOf0(sK15,sdtasasdt0(xI,xJ)) ) )
& aElementOf0(sK14,sdtasasdt0(xI,xJ))
& ! [U_85] :
( aElementOf0(U_85,sdtasasdt0(xI,xJ))
| ~ aElementOf0(U_85,xJ)
| ~ aElementOf0(U_85,xI) )
& ! [U_84] :
( ( aElementOf0(U_84,xJ)
& aElementOf0(U_84,xI) )
| ~ aElementOf0(U_84,sdtasasdt0(xI,xJ)) )
& aSet0(sdtasasdt0(xI,xJ)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_82,sK16)],[f_27_6]) ).
cnf(f_27_8,negated_conjecture,
aSet0(sdtasasdt0(xI,xJ)),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_9,negated_conjecture,
( aElementOf0(U_84,xI)
| ~ aElementOf0(U_84,sdtasasdt0(xI,xJ)) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_10,negated_conjecture,
( aElementOf0(U_84,xJ)
| ~ aElementOf0(U_84,sdtasasdt0(xI,xJ)) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_11,negated_conjecture,
( aElementOf0(U_85,sdtasasdt0(xI,xJ))
| ~ aElementOf0(U_85,xJ)
| ~ aElementOf0(U_85,xI) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_12,negated_conjecture,
aElementOf0(sK14,sdtasasdt0(xI,xJ)),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_13,negated_conjecture,
( aElement0(sK16)
| aElementOf0(sK15,sdtasasdt0(xI,xJ)) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_14,negated_conjecture,
( ~ aElementOf0(sdtasdt0(sK16,sK14),sdtasasdt0(xI,xJ))
| aElementOf0(sK15,sdtasasdt0(xI,xJ)) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_15,negated_conjecture,
( aElement0(sK16)
| ~ aElementOf0(sdtpldt0(sK14,sK15),sdtasasdt0(xI,xJ)) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_16,negated_conjecture,
( ~ aElementOf0(sdtasdt0(sK16,sK14),sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtpldt0(sK14,sK15),sdtasasdt0(xI,xJ)) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_17,negated_conjecture,
~ aIdeal0(sdtasasdt0(xI,xJ)),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_1_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_4]) ).
cnf(f_19_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( smndt0(Eq_x_0) = smndt0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( sdtpldt0(Eq_x_0,Eq_x_1) = sdtpldt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sdtasdt0(Eq_x_0,Eq_x_1) = sdtasdt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sdtpldt1(Eq_x_0,Eq_x_1) = sdtpldt1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sdtasasdt0(Eq_x_0,Eq_x_1) = sdtasasdt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2) = sK9(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( aElement0(Eq_y_0)
| ~ aElement0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( aSet0(Eq_y_0)
| ~ aSet0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( aElementOf0(Eq_y_0,Eq_y_1)
| ~ aElementOf0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( aIdeal0(Eq_y_0)
| ~ aIdeal0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG093+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 20:50:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 82.25/82.55 % SZS status Theorem for theBenchmark
% 82.25/82.55 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------