%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM535+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 : n009.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 08:52:32 AM UTC 2026
% Result : Theorem 237.96s 238.23s
% Output : Proof 238.81s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mSetSort,axiom,
! [W0] :
( aSet0(W0)
=> $true ),
file('theBenchmark.p',mSetSort) ).
fof(mElmSort,axiom,
! [W0] :
( aElement0(W0)
=> $true ),
file('theBenchmark.p',mElmSort) ).
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mFinRel,axiom,
! [W0] :
( aSet0(W0)
=> ( isFinite0(W0)
=> $true ) ),
file('theBenchmark.p',mFinRel) ).
fof(mDefEmp,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('theBenchmark.p',mDefEmp) ).
fof(mEmpFin,axiom,
isFinite0(slcrc0),
file('theBenchmark.p',mEmpFin) ).
fof(mCntRel,axiom,
! [W0] :
( aSet0(W0)
=> ( isCountable0(W0)
=> $true ) ),
file('theBenchmark.p',mCntRel) ).
fof(mCountNFin,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('theBenchmark.p',mCountNFin) ).
fof(mCountNFin_01,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> W0 != slcrc0 ),
file('theBenchmark.p',mCountNFin_01) ).
fof(mDefSub,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
fof(mSubFSet,axiom,
! [W0] :
( ( isFinite0(W0)
& aSet0(W0) )
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('theBenchmark.p',mSubFSet) ).
fof(mSubRefl,axiom,
! [W0] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('theBenchmark.p',mSubRefl) ).
fof(mSubASymm,axiom,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W0)
& aSubsetOf0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mSubASymm) ).
fof(mSubTrans,axiom,
! [W0,W1,W2] :
( ( aSet0(W2)
& aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W2)
& aSubsetOf0(W0,W1) )
=> aSubsetOf0(W0,W2) ) ),
file('theBenchmark.p',mSubTrans) ).
fof(mDefCons,definition,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefCons) ).
fof(mDefDiff,definition,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefDiff) ).
fof(m__617,hypothesis,
aSet0(xS),
file('theBenchmark.p',m__617) ).
fof(m__617_02,hypothesis,
aElementOf0(xx,xS),
file('theBenchmark.p',m__617_02) ).
fof(m__,conjecture,
( ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(W0,xS) ) ) ) )
& ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ) ),
file('theBenchmark.p',m__) ).
fof(f_1_1,plain,
! [W0] :
( $true
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSetSort]) ).
fof(f_1_2,plain,
! [U_0] :
( $true
| ~ aSet0(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_0] : ~ aSet0(U_0)
| $true ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
! [U_0] :
( ~ aSet0(U_0)
| $true ),
inference(definitional_conversion,[status(esa)],[f_1_3]) ).
cnf(f_1_5,plain,
( ~ aSet0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
! [W0] :
( $true
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mElmSort]) ).
fof(f_2_2,plain,
! [U_1] :
( $true
| ~ aElement0(U_1) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_1] : ~ aElement0(U_1)
| $true ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
! [U_1] :
( ~ aElement0(U_1)
| $true ),
inference(definitional_conversion,[status(esa)],[f_2_3]) ).
cnf(f_2_5,plain,
( ~ aElement0(U_1)
| $true ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mEOfElem]) ).
fof(f_3_2,plain,
! [U_3] :
( ! [U_2] :
( aElement0(U_2)
| ~ aElementOf0(U_2,U_3) )
| ~ aSet0(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_3,U_2] :
( aElement0(U_2)
| ~ aElementOf0(U_2,U_3)
| ~ aSet0(U_3) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( aElement0(U_2)
| ~ aElementOf0(U_2,U_3)
| ~ aSet0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [W0] :
( $true
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mFinRel]) ).
fof(f_4_2,plain,
! [U_4] :
( $true
| ~ isFinite0(U_4)
| ~ aSet0(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_4] :
( $true
| ~ isFinite0(U_4)
| ~ aSet0(U_4) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( $true
| ~ isFinite0(U_4)
| ~ aSet0(U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [W0] :
( ( W0 = slcrc0
| ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0) )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(fof_nnf,[status(thm)],[mDefEmp]) ).
fof(f_5_2,plain,
! [U_7] :
( ( U_7 = slcrc0
| ? [U_6] : aElementOf0(U_6,U_7)
| ~ aSet0(U_7) )
& ( ( ! [U_5] : ~ aElementOf0(U_5,U_7)
& aSet0(U_7) )
| U_7 != slcrc0 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_9] :
( U_9 = slcrc0
| ? [U_6] : aElementOf0(U_6,U_9)
| ~ aSet0(U_9) )
& ! [U_8] :
( ( ! [U_5] : ~ aElementOf0(U_5,U_8)
& aSet0(U_8) )
| U_8 != slcrc0 ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_9] :
( U_9 = slcrc0
| aElementOf0(sK1(U_9),U_9)
| ~ aSet0(U_9) )
& ! [U_8] :
( ( ! [U_5] : ~ aElementOf0(U_5,U_8)
& aSet0(U_8) )
| U_8 != slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_6,sK1(U_9))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_5,U_8] :
( ~ aElementOf0(U_5,U_8)
| ~ sP0(U_5,U_8) )
& ! [U_5,U_8] :
( aSet0(U_8)
| ~ sP0(U_5,U_8) )
& ! [U_9] :
( U_9 = slcrc0
| aElementOf0(sK1(U_9),U_9)
| ~ aSet0(U_9) )
& ! [U_5,U_8] :
( sP0(U_5,U_8)
| U_8 != slcrc0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_5_4]) ).
cnf(f_5_6,plain,
( sP0(U_5,U_8)
| U_8 != slcrc0 ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( U_9 = slcrc0
| aElementOf0(sK1(U_9),U_9)
| ~ aSet0(U_9) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_8,plain,
( aSet0(U_8)
| ~ sP0(U_5,U_8) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_9,plain,
( ~ aElementOf0(U_5,U_8)
| ~ sP0(U_5,U_8) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_1,plain,
isFinite0(slcrc0),
inference(fof_nnf,[status(thm)],[mEmpFin]) ).
fof(f_6_2,plain,
isFinite0(slcrc0),
inference(definitional_conversion,[status(esa)],[f_6_1]) ).
cnf(f_6_3,plain,
isFinite0(slcrc0),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [W0] :
( $true
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCntRel]) ).
fof(f_7_2,plain,
! [U_10] :
( $true
| ~ isCountable0(U_10)
| ~ aSet0(U_10) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_10] :
( $true
| ~ isCountable0(U_10)
| ~ aSet0(U_10) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( $true
| ~ isCountable0(U_10)
| ~ aSet0(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCountNFin]) ).
fof(f_8_2,plain,
! [U_11] :
( ~ isFinite0(U_11)
| ~ isCountable0(U_11)
| ~ aSet0(U_11) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_11] :
( ~ isFinite0(U_11)
| ~ isCountable0(U_11)
| ~ aSet0(U_11) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( ~ isFinite0(U_11)
| ~ isCountable0(U_11)
| ~ aSet0(U_11) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [W0] :
( W0 != slcrc0
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mCountNFin_01]) ).
fof(f_9_2,plain,
! [U_12] :
( U_12 != slcrc0
| ~ isCountable0(U_12)
| ~ aSet0(U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_12] :
( U_12 != slcrc0
| ~ isCountable0(U_12)
| ~ aSet0(U_12) ),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
( U_12 != slcrc0
| ~ isCountable0(U_12)
| ~ aSet0(U_12) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [W0] :
( ! [W1] :
( ( aSubsetOf0(W1,W0)
| ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSub]) ).
fof(f_10_2,plain,
! [U_16] :
( ! [U_15] :
( ( aSubsetOf0(U_15,U_16)
| ? [U_14] :
( ~ aElementOf0(U_14,U_16)
& aElementOf0(U_14,U_15) )
| ~ aSet0(U_15) )
& ( ( ! [U_13] :
( aElementOf0(U_13,U_16)
| ~ aElementOf0(U_13,U_15) )
& aSet0(U_15) )
| ~ aSubsetOf0(U_15,U_16) ) )
| ~ aSet0(U_16) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_16] :
( ( ! [U_18] :
( aSubsetOf0(U_18,U_16)
| ? [U_14] :
( ~ aElementOf0(U_14,U_16)
& aElementOf0(U_14,U_18) )
| ~ aSet0(U_18) )
& ! [U_17] :
( ( ! [U_13] :
( aElementOf0(U_13,U_16)
| ~ aElementOf0(U_13,U_17) )
& aSet0(U_17) )
| ~ aSubsetOf0(U_17,U_16) ) )
| ~ aSet0(U_16) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
! [U_16] :
( ( ! [U_18] :
( aSubsetOf0(U_18,U_16)
| ( ~ aElementOf0(sK2(U_16,U_18),U_16)
& aElementOf0(sK2(U_16,U_18),U_18) )
| ~ aSet0(U_18) )
& ! [U_17] :
( ( ! [U_13] :
( aElementOf0(U_13,U_16)
| ~ aElementOf0(U_13,U_17) )
& aSet0(U_17) )
| ~ aSubsetOf0(U_17,U_16) ) )
| ~ aSet0(U_16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_14,sK2(U_16,U_18))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_16,U_18] :
( ~ aElementOf0(sK2(U_16,U_18),U_16)
| ~ sP2(U_16,U_18) )
& ! [U_16,U_18] :
( aElementOf0(sK2(U_16,U_18),U_18)
| ~ sP2(U_16,U_18) )
& ! [U_13,U_16,U_17] :
( aElementOf0(U_13,U_16)
| ~ aElementOf0(U_13,U_17)
| ~ sP1(U_13,U_16,U_17) )
& ! [U_13,U_16,U_17] :
( aSet0(U_17)
| ~ sP1(U_13,U_16,U_17) )
& ! [U_13,U_16,U_18,U_17] :
( aSubsetOf0(U_18,U_16)
| sP2(U_16,U_18)
| ~ aSet0(U_18)
| ~ sP3(U_13,U_16,U_18,U_17) )
& ! [U_13,U_16,U_18,U_17] :
( sP1(U_13,U_16,U_17)
| ~ aSubsetOf0(U_17,U_16)
| ~ sP3(U_13,U_16,U_18,U_17) )
& ! [U_13,U_16,U_18,U_17] :
( sP3(U_13,U_16,U_18,U_17)
| ~ aSet0(U_16) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2,sP3])],[f_10_4]) ).
cnf(f_10_6,plain,
( sP3(U_13,U_16,U_18,U_17)
| ~ aSet0(U_16) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( sP1(U_13,U_16,U_17)
| ~ aSubsetOf0(U_17,U_16)
| ~ sP3(U_13,U_16,U_18,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( aSubsetOf0(U_18,U_16)
| sP2(U_16,U_18)
| ~ aSet0(U_18)
| ~ sP3(U_13,U_16,U_18,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( aSet0(U_17)
| ~ sP1(U_13,U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_10,plain,
( aElementOf0(U_13,U_16)
| ~ aElementOf0(U_13,U_17)
| ~ sP1(U_13,U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_11,plain,
( aElementOf0(sK2(U_16,U_18),U_18)
| ~ sP2(U_16,U_18) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_12,plain,
( ~ aElementOf0(sK2(U_16,U_18),U_16)
| ~ sP2(U_16,U_18) ),
inference(clausify,[status(thm)],[f_10_5]) ).
fof(f_11_1,plain,
! [W0] :
( ! [W1] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSubFSet]) ).
fof(f_11_2,plain,
! [U_20] :
( ! [U_19] :
( isFinite0(U_19)
| ~ aSubsetOf0(U_19,U_20) )
| ~ isFinite0(U_20)
| ~ aSet0(U_20) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_20,U_19] :
( isFinite0(U_19)
| ~ aSubsetOf0(U_19,U_20)
| ~ isFinite0(U_20)
| ~ aSet0(U_20) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( isFinite0(U_19)
| ~ aSubsetOf0(U_19,U_20)
| ~ isFinite0(U_20)
| ~ aSet0(U_20) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [W0] :
( aSubsetOf0(W0,W0)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSubRefl]) ).
fof(f_12_2,plain,
! [U_21] :
( aSubsetOf0(U_21,U_21)
| ~ aSet0(U_21) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_21] :
( aSubsetOf0(U_21,U_21)
| ~ aSet0(U_21) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( aSubsetOf0(U_21,U_21)
| ~ aSet0(U_21) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [W0,W1] :
( W0 = W1
| ~ aSubsetOf0(W1,W0)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSubASymm]) ).
fof(f_13_2,plain,
! [U_23,U_22] :
( U_23 = U_22
| ~ aSubsetOf0(U_22,U_23)
| ~ aSubsetOf0(U_23,U_22)
| ~ aSet0(U_22)
| ~ aSet0(U_23) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_23,U_22] :
( U_23 = U_22
| ~ aSubsetOf0(U_22,U_23)
| ~ aSubsetOf0(U_23,U_22)
| ~ aSet0(U_22)
| ~ aSet0(U_23) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( U_23 = U_22
| ~ aSubsetOf0(U_22,U_23)
| ~ aSubsetOf0(U_23,U_22)
| ~ aSet0(U_22)
| ~ aSet0(U_23) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [W0,W1,W2] :
( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mSubTrans]) ).
fof(f_14_2,plain,
! [U_26,U_25,U_24] :
( aSubsetOf0(U_26,U_24)
| ~ aSubsetOf0(U_25,U_24)
| ~ aSubsetOf0(U_26,U_25)
| ~ aSet0(U_24)
| ~ aSet0(U_25)
| ~ aSet0(U_26) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_24,U_25,U_26] :
( aSubsetOf0(U_26,U_24)
| ~ aSubsetOf0(U_25,U_24)
| ~ aSubsetOf0(U_26,U_25)
| ~ aSet0(U_24)
| ~ aSet0(U_25)
| ~ aSet0(U_26) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( aSubsetOf0(U_26,U_24)
| ~ aSubsetOf0(U_25,U_24)
| ~ aSubsetOf0(U_26,U_25)
| ~ aSet0(U_24)
| ~ aSet0(U_25)
| ~ aSet0(U_26) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtpldt0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ( ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3) )
& ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefCons]) ).
fof(f_15_2,plain,
! [U_31,U_30] :
( ! [U_29] :
( ( U_29 = sdtpldt0(U_31,U_30)
| ? [U_28] :
( ( ~ aElementOf0(U_28,U_29)
& ( U_28 = U_30
| aElementOf0(U_28,U_31) )
& aElement0(U_28) )
| ( ( ( U_28 != U_30
& ~ aElementOf0(U_28,U_31) )
| ~ aElement0(U_28) )
& aElementOf0(U_28,U_29) ) )
| ~ aSet0(U_29) )
& ( ( ! [U_27] :
( ( aElementOf0(U_27,U_29)
| ( U_27 != U_30
& ~ aElementOf0(U_27,U_31) )
| ~ aElement0(U_27) )
& ( ( ( U_27 = U_30
| aElementOf0(U_27,U_31) )
& aElement0(U_27) )
| ~ aElementOf0(U_27,U_29) ) )
& aSet0(U_29) )
| U_29 != sdtpldt0(U_31,U_30) ) )
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_31,U_30] :
( ( ! [U_37] :
( U_37 = sdtpldt0(U_31,U_30)
| ? [U_35] :
( ~ aElementOf0(U_35,U_37)
& ( U_35 = U_30
| aElementOf0(U_35,U_31) )
& aElement0(U_35) )
| ? [U_34] :
( ( ( U_34 != U_30
& ~ aElementOf0(U_34,U_31) )
| ~ aElement0(U_34) )
& aElementOf0(U_34,U_37) )
| ~ aSet0(U_37) )
& ! [U_36] :
( ( ! [U_33] :
( aElementOf0(U_33,U_36)
| ( U_33 != U_30
& ~ aElementOf0(U_33,U_31) )
| ~ aElement0(U_33) )
& ! [U_32] :
( ( ( U_32 = U_30
| aElementOf0(U_32,U_31) )
& aElement0(U_32) )
| ~ aElementOf0(U_32,U_36) )
& aSet0(U_36) )
| U_36 != sdtpldt0(U_31,U_30) ) )
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
! [U_31,U_30] :
( ( ! [U_37] :
( U_37 = sdtpldt0(U_31,U_30)
| ? [U_35] :
( ~ aElementOf0(U_35,U_37)
& ( U_35 = U_30
| aElementOf0(U_35,U_31) )
& aElement0(U_35) )
| ( ( ( sK3(U_31,U_30,U_37) != U_30
& ~ aElementOf0(sK3(U_31,U_30,U_37),U_31) )
| ~ aElement0(sK3(U_31,U_30,U_37)) )
& aElementOf0(sK3(U_31,U_30,U_37),U_37) )
| ~ aSet0(U_37) )
& ! [U_36] :
( ( ! [U_33] :
( aElementOf0(U_33,U_36)
| ( U_33 != U_30
& ~ aElementOf0(U_33,U_31) )
| ~ aElement0(U_33) )
& ! [U_32] :
( ( ( U_32 = U_30
| aElementOf0(U_32,U_31) )
& aElement0(U_32) )
| ~ aElementOf0(U_32,U_36) )
& aSet0(U_36) )
| U_36 != sdtpldt0(U_31,U_30) ) )
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_34,sK3(U_31,U_30,U_37))],[f_15_3]) ).
fof(f_15_5,plain,
! [U_31,U_30] :
( ( ! [U_37] :
( U_37 = sdtpldt0(U_31,U_30)
| ( ~ aElementOf0(sK4(U_31,U_30,U_37),U_37)
& ( sK4(U_31,U_30,U_37) = U_30
| aElementOf0(sK4(U_31,U_30,U_37),U_31) )
& aElement0(sK4(U_31,U_30,U_37)) )
| ( ( ( sK3(U_31,U_30,U_37) != U_30
& ~ aElementOf0(sK3(U_31,U_30,U_37),U_31) )
| ~ aElement0(sK3(U_31,U_30,U_37)) )
& aElementOf0(sK3(U_31,U_30,U_37),U_37) )
| ~ aSet0(U_37) )
& ! [U_36] :
( ( ! [U_33] :
( aElementOf0(U_33,U_36)
| ( U_33 != U_30
& ~ aElementOf0(U_33,U_31) )
| ~ aElement0(U_33) )
& ! [U_32] :
( ( ( U_32 = U_30
| aElementOf0(U_32,U_31) )
& aElement0(U_32) )
| ~ aElementOf0(U_32,U_36) )
& aSet0(U_36) )
| U_36 != sdtpldt0(U_31,U_30) ) )
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_35,sK4(U_31,U_30,U_37))],[f_15_4]) ).
fof(f_15_6,plain,
( ! [U_30,U_37,U_31] :
( ~ aElementOf0(sK4(U_31,U_30,U_37),U_37)
| ~ sP9(U_30,U_37,U_31) )
& ! [U_30,U_37,U_31] :
( sK4(U_31,U_30,U_37) = U_30
| aElementOf0(sK4(U_31,U_30,U_37),U_31)
| ~ sP9(U_30,U_37,U_31) )
& ! [U_30,U_37,U_31] :
( aElement0(sK4(U_31,U_30,U_37))
| ~ sP9(U_30,U_37,U_31) )
& ! [U_30,U_37,U_31] :
( sK3(U_31,U_30,U_37) != U_30
| ~ sP7(U_30,U_37,U_31) )
& ! [U_30,U_37,U_31] :
( ~ aElementOf0(sK3(U_31,U_30,U_37),U_31)
| ~ sP7(U_30,U_37,U_31) )
& ! [U_30,U_37,U_31] :
( sP7(U_30,U_37,U_31)
| ~ aElement0(sK3(U_31,U_30,U_37))
| ~ sP8(U_30,U_37,U_31) )
& ! [U_30,U_37,U_31] :
( aElementOf0(sK3(U_31,U_30,U_37),U_37)
| ~ sP8(U_30,U_37,U_31) )
& ! [U_30,U_31,U_33] :
( U_33 != U_30
| ~ sP5(U_30,U_31,U_33) )
& ! [U_30,U_31,U_33] :
( ~ aElementOf0(U_33,U_31)
| ~ sP5(U_30,U_31,U_33) )
& ! [U_30,U_31,U_32] :
( U_32 = U_30
| aElementOf0(U_32,U_31)
| ~ sP4(U_30,U_31,U_32) )
& ! [U_30,U_31,U_32] :
( aElement0(U_32)
| ~ sP4(U_30,U_31,U_32) )
& ! [U_30,U_31,U_32,U_33,U_36] :
( aElementOf0(U_33,U_36)
| sP5(U_30,U_31,U_33)
| ~ aElement0(U_33)
| ~ sP6(U_30,U_31,U_32,U_33,U_36) )
& ! [U_30,U_31,U_32,U_33,U_36] :
( sP4(U_30,U_31,U_32)
| ~ aElementOf0(U_32,U_36)
| ~ sP6(U_30,U_31,U_32,U_33,U_36) )
& ! [U_30,U_31,U_32,U_33,U_36] :
( aSet0(U_36)
| ~ sP6(U_30,U_31,U_32,U_33,U_36) )
& ! [U_30,U_37,U_31,U_32,U_33,U_36] :
( U_37 = sdtpldt0(U_31,U_30)
| sP9(U_30,U_37,U_31)
| sP8(U_30,U_37,U_31)
| ~ aSet0(U_37)
| ~ sP10(U_30,U_37,U_31,U_32,U_33,U_36) )
& ! [U_30,U_37,U_31,U_32,U_33,U_36] :
( sP6(U_30,U_31,U_32,U_33,U_36)
| U_36 != sdtpldt0(U_31,U_30)
| ~ sP10(U_30,U_37,U_31,U_32,U_33,U_36) )
& ! [U_30,U_37,U_31,U_32,U_33,U_36] :
( sP10(U_30,U_37,U_31,U_32,U_33,U_36)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4,sP5,sP6,sP7,sP8,sP9,sP10])],[f_15_5]) ).
cnf(f_15_7,plain,
( sP10(U_30,U_37,U_31,U_32,U_33,U_36)
| ~ aElement0(U_30)
| ~ aSet0(U_31) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_8,plain,
( sP6(U_30,U_31,U_32,U_33,U_36)
| U_36 != sdtpldt0(U_31,U_30)
| ~ sP10(U_30,U_37,U_31,U_32,U_33,U_36) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_9,plain,
( U_37 = sdtpldt0(U_31,U_30)
| sP9(U_30,U_37,U_31)
| sP8(U_30,U_37,U_31)
| ~ aSet0(U_37)
| ~ sP10(U_30,U_37,U_31,U_32,U_33,U_36) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_10,plain,
( aSet0(U_36)
| ~ sP6(U_30,U_31,U_32,U_33,U_36) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_11,plain,
( sP4(U_30,U_31,U_32)
| ~ aElementOf0(U_32,U_36)
| ~ sP6(U_30,U_31,U_32,U_33,U_36) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_12,plain,
( aElementOf0(U_33,U_36)
| sP5(U_30,U_31,U_33)
| ~ aElement0(U_33)
| ~ sP6(U_30,U_31,U_32,U_33,U_36) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_13,plain,
( aElement0(U_32)
| ~ sP4(U_30,U_31,U_32) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_14,plain,
( U_32 = U_30
| aElementOf0(U_32,U_31)
| ~ sP4(U_30,U_31,U_32) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_15,plain,
( ~ aElementOf0(U_33,U_31)
| ~ sP5(U_30,U_31,U_33) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_16,plain,
( U_33 != U_30
| ~ sP5(U_30,U_31,U_33) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_17,plain,
( aElementOf0(sK3(U_31,U_30,U_37),U_37)
| ~ sP8(U_30,U_37,U_31) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_18,plain,
( sP7(U_30,U_37,U_31)
| ~ aElement0(sK3(U_31,U_30,U_37))
| ~ sP8(U_30,U_37,U_31) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_19,plain,
( ~ aElementOf0(sK3(U_31,U_30,U_37),U_31)
| ~ sP7(U_30,U_37,U_31) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_20,plain,
( sK3(U_31,U_30,U_37) != U_30
| ~ sP7(U_30,U_37,U_31) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_21,plain,
( aElement0(sK4(U_31,U_30,U_37))
| ~ sP9(U_30,U_37,U_31) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_22,plain,
( sK4(U_31,U_30,U_37) = U_30
| aElementOf0(sK4(U_31,U_30,U_37),U_31)
| ~ sP9(U_30,U_37,U_31) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_23,plain,
( ~ aElementOf0(sK4(U_31,U_30,U_37),U_37)
| ~ sP9(U_30,U_37,U_31) ),
inference(clausify,[status(thm)],[f_15_6]) ).
fof(f_16_1,plain,
! [W0,W1] :
( ! [W2] :
( ( W2 = sdtmndt0(W0,W1)
| ? [W3] :
( ( ~ aElementOf0(W3,W2)
& W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ( ( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3) )
& aElementOf0(W3,W2) ) )
| ~ aSet0(W2) )
& ( ( ! [W3] :
( ( aElementOf0(W3,W2)
| W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3) )
& ( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefDiff]) ).
fof(f_16_2,plain,
! [U_42,U_41] :
( ! [U_40] :
( ( U_40 = sdtmndt0(U_42,U_41)
| ? [U_39] :
( ( ~ aElementOf0(U_39,U_40)
& U_39 != U_41
& aElementOf0(U_39,U_42)
& aElement0(U_39) )
| ( ( U_39 = U_41
| ~ aElementOf0(U_39,U_42)
| ~ aElement0(U_39) )
& aElementOf0(U_39,U_40) ) )
| ~ aSet0(U_40) )
& ( ( ! [U_38] :
( ( aElementOf0(U_38,U_40)
| U_38 = U_41
| ~ aElementOf0(U_38,U_42)
| ~ aElement0(U_38) )
& ( ( U_38 != U_41
& aElementOf0(U_38,U_42)
& aElement0(U_38) )
| ~ aElementOf0(U_38,U_40) ) )
& aSet0(U_40) )
| U_40 != sdtmndt0(U_42,U_41) ) )
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_42,U_41] :
( ( ! [U_48] :
( U_48 = sdtmndt0(U_42,U_41)
| ? [U_46] :
( ~ aElementOf0(U_46,U_48)
& U_46 != U_41
& aElementOf0(U_46,U_42)
& aElement0(U_46) )
| ? [U_45] :
( ( U_45 = U_41
| ~ aElementOf0(U_45,U_42)
| ~ aElement0(U_45) )
& aElementOf0(U_45,U_48) )
| ~ aSet0(U_48) )
& ! [U_47] :
( ( ! [U_44] :
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44) )
& ! [U_43] :
( ( U_43 != U_41
& aElementOf0(U_43,U_42)
& aElement0(U_43) )
| ~ aElementOf0(U_43,U_47) )
& aSet0(U_47) )
| U_47 != sdtmndt0(U_42,U_41) ) )
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_42,U_41] :
( ( ! [U_48] :
( U_48 = sdtmndt0(U_42,U_41)
| ? [U_46] :
( ~ aElementOf0(U_46,U_48)
& U_46 != U_41
& aElementOf0(U_46,U_42)
& aElement0(U_46) )
| ( ( sK5(U_42,U_41,U_48) = U_41
| ~ aElementOf0(sK5(U_42,U_41,U_48),U_42)
| ~ aElement0(sK5(U_42,U_41,U_48)) )
& aElementOf0(sK5(U_42,U_41,U_48),U_48) )
| ~ aSet0(U_48) )
& ! [U_47] :
( ( ! [U_44] :
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44) )
& ! [U_43] :
( ( U_43 != U_41
& aElementOf0(U_43,U_42)
& aElement0(U_43) )
| ~ aElementOf0(U_43,U_47) )
& aSet0(U_47) )
| U_47 != sdtmndt0(U_42,U_41) ) )
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_45,sK5(U_42,U_41,U_48))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_42,U_41] :
( ( ! [U_48] :
( U_48 = sdtmndt0(U_42,U_41)
| ( ~ aElementOf0(sK6(U_42,U_41,U_48),U_48)
& sK6(U_42,U_41,U_48) != U_41
& aElementOf0(sK6(U_42,U_41,U_48),U_42)
& aElement0(sK6(U_42,U_41,U_48)) )
| ( ( sK5(U_42,U_41,U_48) = U_41
| ~ aElementOf0(sK5(U_42,U_41,U_48),U_42)
| ~ aElement0(sK5(U_42,U_41,U_48)) )
& aElementOf0(sK5(U_42,U_41,U_48),U_48) )
| ~ aSet0(U_48) )
& ! [U_47] :
( ( ! [U_44] :
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44) )
& ! [U_43] :
( ( U_43 != U_41
& aElementOf0(U_43,U_42)
& aElement0(U_43) )
| ~ aElementOf0(U_43,U_47) )
& aSet0(U_47) )
| U_47 != sdtmndt0(U_42,U_41) ) )
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_46,sK6(U_42,U_41,U_48))],[f_16_4]) ).
fof(f_16_6,plain,
( ! [U_48,U_42,U_41] :
( ~ aElementOf0(sK6(U_42,U_41,U_48),U_48)
| ~ sP14(U_48,U_42,U_41) )
& ! [U_48,U_42,U_41] :
( sK6(U_42,U_41,U_48) != U_41
| ~ sP14(U_48,U_42,U_41) )
& ! [U_48,U_42,U_41] :
( aElementOf0(sK6(U_42,U_41,U_48),U_42)
| ~ sP14(U_48,U_42,U_41) )
& ! [U_48,U_42,U_41] :
( aElement0(sK6(U_42,U_41,U_48))
| ~ sP14(U_48,U_42,U_41) )
& ! [U_48,U_42,U_41] :
( sK5(U_42,U_41,U_48) = U_41
| ~ aElementOf0(sK5(U_42,U_41,U_48),U_42)
| ~ aElement0(sK5(U_42,U_41,U_48))
| ~ sP13(U_48,U_42,U_41) )
& ! [U_48,U_42,U_41] :
( aElementOf0(sK5(U_42,U_41,U_48),U_48)
| ~ sP13(U_48,U_42,U_41) )
& ! [U_43,U_42,U_41] :
( U_43 != U_41
| ~ sP11(U_43,U_42,U_41) )
& ! [U_43,U_42,U_41] :
( aElementOf0(U_43,U_42)
| ~ sP11(U_43,U_42,U_41) )
& ! [U_43,U_42,U_41] :
( aElement0(U_43)
| ~ sP11(U_43,U_42,U_41) )
& ! [U_44,U_43,U_42,U_47,U_41] :
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44)
| ~ sP12(U_44,U_43,U_42,U_47,U_41) )
& ! [U_44,U_43,U_42,U_47,U_41] :
( sP11(U_43,U_42,U_41)
| ~ aElementOf0(U_43,U_47)
| ~ sP12(U_44,U_43,U_42,U_47,U_41) )
& ! [U_44,U_43,U_42,U_47,U_41] :
( aSet0(U_47)
| ~ sP12(U_44,U_43,U_42,U_47,U_41) )
& ! [U_44,U_48,U_43,U_42,U_47,U_41] :
( U_48 = sdtmndt0(U_42,U_41)
| sP14(U_48,U_42,U_41)
| sP13(U_48,U_42,U_41)
| ~ aSet0(U_48)
| ~ sP15(U_44,U_48,U_43,U_42,U_47,U_41) )
& ! [U_44,U_48,U_43,U_42,U_47,U_41] :
( sP12(U_44,U_43,U_42,U_47,U_41)
| U_47 != sdtmndt0(U_42,U_41)
| ~ sP15(U_44,U_48,U_43,U_42,U_47,U_41) )
& ! [U_44,U_48,U_43,U_42,U_47,U_41] :
( sP15(U_44,U_48,U_43,U_42,U_47,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11,sP12,sP13,sP14,sP15])],[f_16_5]) ).
cnf(f_16_7,plain,
( sP15(U_44,U_48,U_43,U_42,U_47,U_41)
| ~ aElement0(U_41)
| ~ aSet0(U_42) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_8,plain,
( sP12(U_44,U_43,U_42,U_47,U_41)
| U_47 != sdtmndt0(U_42,U_41)
| ~ sP15(U_44,U_48,U_43,U_42,U_47,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_9,plain,
( U_48 = sdtmndt0(U_42,U_41)
| sP14(U_48,U_42,U_41)
| sP13(U_48,U_42,U_41)
| ~ aSet0(U_48)
| ~ sP15(U_44,U_48,U_43,U_42,U_47,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_10,plain,
( aSet0(U_47)
| ~ sP12(U_44,U_43,U_42,U_47,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_11,plain,
( sP11(U_43,U_42,U_41)
| ~ aElementOf0(U_43,U_47)
| ~ sP12(U_44,U_43,U_42,U_47,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_12,plain,
( aElementOf0(U_44,U_47)
| U_44 = U_41
| ~ aElementOf0(U_44,U_42)
| ~ aElement0(U_44)
| ~ sP12(U_44,U_43,U_42,U_47,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_13,plain,
( aElement0(U_43)
| ~ sP11(U_43,U_42,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_14,plain,
( aElementOf0(U_43,U_42)
| ~ sP11(U_43,U_42,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_15,plain,
( U_43 != U_41
| ~ sP11(U_43,U_42,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_16,plain,
( aElementOf0(sK5(U_42,U_41,U_48),U_48)
| ~ sP13(U_48,U_42,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_17,plain,
( sK5(U_42,U_41,U_48) = U_41
| ~ aElementOf0(sK5(U_42,U_41,U_48),U_42)
| ~ aElement0(sK5(U_42,U_41,U_48))
| ~ sP13(U_48,U_42,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_18,plain,
( aElement0(sK6(U_42,U_41,U_48))
| ~ sP14(U_48,U_42,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_19,plain,
( aElementOf0(sK6(U_42,U_41,U_48),U_42)
| ~ sP14(U_48,U_42,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_20,plain,
( sK6(U_42,U_41,U_48) != U_41
| ~ sP14(U_48,U_42,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_21,plain,
( ~ aElementOf0(sK6(U_42,U_41,U_48),U_48)
| ~ sP14(U_48,U_42,U_41) ),
inference(clausify,[status(thm)],[f_16_6]) ).
fof(f_17_1,plain,
aSet0(xS),
inference(fof_nnf,[status(thm)],[m__617]) ).
fof(f_17_2,plain,
aSet0(xS),
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,plain,
aSet0(xS),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
aElementOf0(xx,xS),
inference(fof_nnf,[status(thm)],[m__617_02]) ).
fof(f_18_2,plain,
aElementOf0(xx,xS),
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,plain,
aElementOf0(xx,xS),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,negated_conjecture,
~ ( ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(W0,xS) ) ) ) )
& ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_19_2,negated_conjecture,
( ( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [W0] :
( ( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0) )
& ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( ( aElementOf0(W0,sdtmndt0(xS,xx))
| W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0) )
& ( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx)) )
| ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( ( aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElement0(W0) )
& ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xS,xx)) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [W0] :
( ( aElementOf0(W0,sdtmndt0(xS,xx))
| W0 = xx
| ~ aElementOf0(W0,xS)
| ~ aElement0(W0) )
& ( ( W0 != xx
& aElementOf0(W0,xS)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx)) ) ),
inference(fof_nnf,[status(thm)],[f_19_1]) ).
fof(f_19_3,negated_conjecture,
( ( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [U_54] :
( ~ aElementOf0(U_54,xS)
& aElementOf0(U_54,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [U_53] :
( ( aElementOf0(U_53,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( U_53 != xx
& ~ aElementOf0(U_53,sdtmndt0(xS,xx)) )
| ~ aElement0(U_53) )
& ( ( ( U_53 = xx
| aElementOf0(U_53,sdtmndt0(xS,xx)) )
& aElement0(U_53) )
| ~ aElementOf0(U_53,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [U_52] :
( ( aElementOf0(U_52,sdtmndt0(xS,xx))
| U_52 = xx
| ~ aElementOf0(U_52,xS)
| ~ aElement0(U_52) )
& ( ( U_52 != xx
& aElementOf0(U_52,xS)
& aElement0(U_52) )
| ~ aElementOf0(U_52,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx)) )
| ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [U_51] :
( ~ aElementOf0(U_51,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(U_51,xS) )
& ! [U_50] :
( ( aElementOf0(U_50,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( U_50 != xx
& ~ aElementOf0(U_50,sdtmndt0(xS,xx)) )
| ~ aElement0(U_50) )
& ( ( ( U_50 = xx
| aElementOf0(U_50,sdtmndt0(xS,xx)) )
& aElement0(U_50) )
| ~ aElementOf0(U_50,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [U_49] :
( ( aElementOf0(U_49,sdtmndt0(xS,xx))
| U_49 = xx
| ~ aElementOf0(U_49,xS)
| ~ aElement0(U_49) )
& ( ( U_49 != xx
& aElementOf0(U_49,xS)
& aElement0(U_49) )
| ~ aElementOf0(U_49,sdtmndt0(xS,xx)) ) )
& aSet0(sdtmndt0(xS,xx)) ) ),
inference(variable_rename,[status(thm)],[f_19_2]) ).
fof(f_19_4,negated_conjecture,
( ( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [U_54] :
( ~ aElementOf0(U_54,xS)
& aElementOf0(U_54,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [U_62] :
( aElementOf0(U_62,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( U_62 != xx
& ~ aElementOf0(U_62,sdtmndt0(xS,xx)) )
| ~ aElement0(U_62) )
& ! [U_61] :
( ( ( U_61 = xx
| aElementOf0(U_61,sdtmndt0(xS,xx)) )
& aElement0(U_61) )
| ~ aElementOf0(U_61,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [U_60] :
( aElementOf0(U_60,sdtmndt0(xS,xx))
| U_60 = xx
| ~ aElementOf0(U_60,xS)
| ~ aElement0(U_60) )
& ! [U_59] :
( ( U_59 != xx
& aElementOf0(U_59,xS)
& aElement0(U_59) )
| ~ aElementOf0(U_59,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) )
| ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [U_51] :
( ~ aElementOf0(U_51,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(U_51,xS) )
& ! [U_58] :
( aElementOf0(U_58,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( U_58 != xx
& ~ aElementOf0(U_58,sdtmndt0(xS,xx)) )
| ~ aElement0(U_58) )
& ! [U_57] :
( ( ( U_57 = xx
| aElementOf0(U_57,sdtmndt0(xS,xx)) )
& aElement0(U_57) )
| ~ aElementOf0(U_57,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [U_56] :
( aElementOf0(U_56,sdtmndt0(xS,xx))
| U_56 = xx
| ~ aElementOf0(U_56,xS)
| ~ aElement0(U_56) )
& ! [U_55] :
( ( U_55 != xx
& aElementOf0(U_55,xS)
& aElement0(U_55) )
| ~ aElementOf0(U_55,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) ) ),
inference(miniscope,[status(thm)],[f_19_3]) ).
fof(f_19_5,negated_conjecture,
( ( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [U_54] :
( ~ aElementOf0(U_54,xS)
& aElementOf0(U_54,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& ! [U_62] :
( aElementOf0(U_62,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( U_62 != xx
& ~ aElementOf0(U_62,sdtmndt0(xS,xx)) )
| ~ aElement0(U_62) )
& ! [U_61] :
( ( ( U_61 = xx
| aElementOf0(U_61,sdtmndt0(xS,xx)) )
& aElement0(U_61) )
| ~ aElementOf0(U_61,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [U_60] :
( aElementOf0(U_60,sdtmndt0(xS,xx))
| U_60 = xx
| ~ aElementOf0(U_60,xS)
| ~ aElement0(U_60) )
& ! [U_59] :
( ( U_59 != xx
& aElementOf0(U_59,xS)
& aElement0(U_59) )
| ~ aElementOf0(U_59,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) )
| ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aElementOf0(sK7,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(sK7,xS)
& ! [U_58] :
( aElementOf0(U_58,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( U_58 != xx
& ~ aElementOf0(U_58,sdtmndt0(xS,xx)) )
| ~ aElement0(U_58) )
& ! [U_57] :
( ( ( U_57 = xx
| aElementOf0(U_57,sdtmndt0(xS,xx)) )
& aElement0(U_57) )
| ~ aElementOf0(U_57,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [U_56] :
( aElementOf0(U_56,sdtmndt0(xS,xx))
| U_56 = xx
| ~ aElementOf0(U_56,xS)
| ~ aElement0(U_56) )
& ! [U_55] :
( ( U_55 != xx
& aElementOf0(U_55,xS)
& aElement0(U_55) )
| ~ aElementOf0(U_55,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_51,sK7)],[f_19_4]) ).
fof(f_19_6,negated_conjecture,
( ( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ~ aElementOf0(sK8,xS)
& aElementOf0(sK8,sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [U_62] :
( aElementOf0(U_62,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( U_62 != xx
& ~ aElementOf0(U_62,sdtmndt0(xS,xx)) )
| ~ aElement0(U_62) )
& ! [U_61] :
( ( ( U_61 = xx
| aElementOf0(U_61,sdtmndt0(xS,xx)) )
& aElement0(U_61) )
| ~ aElementOf0(U_61,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [U_60] :
( aElementOf0(U_60,sdtmndt0(xS,xx))
| U_60 = xx
| ~ aElementOf0(U_60,xS)
| ~ aElement0(U_60) )
& ! [U_59] :
( ( U_59 != xx
& aElementOf0(U_59,xS)
& aElement0(U_59) )
| ~ aElementOf0(U_59,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) )
| ( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aElementOf0(sK7,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(sK7,xS)
& ! [U_58] :
( aElementOf0(U_58,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( U_58 != xx
& ~ aElementOf0(U_58,sdtmndt0(xS,xx)) )
| ~ aElement0(U_58) )
& ! [U_57] :
( ( ( U_57 = xx
| aElementOf0(U_57,sdtmndt0(xS,xx)) )
& aElement0(U_57) )
| ~ aElementOf0(U_57,sdtpldt0(sdtmndt0(xS,xx),xx)) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ! [U_56] :
( aElementOf0(U_56,sdtmndt0(xS,xx))
| U_56 = xx
| ~ aElementOf0(U_56,xS)
| ~ aElement0(U_56) )
& ! [U_55] :
( ( U_55 != xx
& aElementOf0(U_55,xS)
& aElement0(U_55) )
| ~ aElementOf0(U_55,sdtmndt0(xS,xx)) )
& aSet0(sdtmndt0(xS,xx)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_54,sK8)],[f_19_5]) ).
fof(f_19_7,negated_conjecture,
( ! [U_62] :
( U_62 != xx
| ~ sP22(U_62) )
& ! [U_62] :
( ~ aElementOf0(U_62,sdtmndt0(xS,xx))
| ~ sP22(U_62) )
& ! [U_61] :
( U_61 = xx
| aElementOf0(U_61,sdtmndt0(xS,xx))
| ~ sP21(U_61) )
& ! [U_61] :
( aElement0(U_61)
| ~ sP21(U_61) )
& ! [U_59] :
( U_59 != xx
| ~ sP20(U_59) )
& ! [U_59] :
( aElementOf0(U_59,xS)
| ~ sP20(U_59) )
& ! [U_59] :
( aElement0(U_59)
| ~ sP20(U_59) )
& ! [U_61,U_60,U_62,U_59] :
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ sP23(U_61,U_60,U_62,U_59) )
& ! [U_61,U_60,U_62,U_59] :
( ~ aElementOf0(sK8,xS)
| ~ sP23(U_61,U_60,U_62,U_59) )
& ! [U_61,U_60,U_62,U_59] :
( aElementOf0(sK8,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP23(U_61,U_60,U_62,U_59) )
& ! [U_61,U_60,U_62,U_59] :
( aElementOf0(U_62,sdtpldt0(sdtmndt0(xS,xx),xx))
| sP22(U_62)
| ~ aElement0(U_62)
| ~ sP23(U_61,U_60,U_62,U_59) )
& ! [U_61,U_60,U_62,U_59] :
( sP21(U_61)
| ~ aElementOf0(U_61,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP23(U_61,U_60,U_62,U_59) )
& ! [U_61,U_60,U_62,U_59] :
( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP23(U_61,U_60,U_62,U_59) )
& ! [U_61,U_60,U_62,U_59] :
( aElementOf0(U_60,sdtmndt0(xS,xx))
| U_60 = xx
| ~ aElementOf0(U_60,xS)
| ~ aElement0(U_60)
| ~ sP23(U_61,U_60,U_62,U_59) )
& ! [U_61,U_60,U_62,U_59] :
( sP20(U_59)
| ~ aElementOf0(U_59,sdtmndt0(xS,xx))
| ~ sP23(U_61,U_60,U_62,U_59) )
& ! [U_61,U_60,U_62,U_59] :
( aSet0(sdtmndt0(xS,xx))
| ~ sP23(U_61,U_60,U_62,U_59) )
& ! [U_58] :
( U_58 != xx
| ~ sP18(U_58) )
& ! [U_58] :
( ~ aElementOf0(U_58,sdtmndt0(xS,xx))
| ~ sP18(U_58) )
& ! [U_57] :
( U_57 = xx
| aElementOf0(U_57,sdtmndt0(xS,xx))
| ~ sP17(U_57) )
& ! [U_57] :
( aElement0(U_57)
| ~ sP17(U_57) )
& ! [U_55] :
( U_55 != xx
| ~ sP16(U_55) )
& ! [U_55] :
( aElementOf0(U_55,xS)
| ~ sP16(U_55) )
& ! [U_55] :
( aElement0(U_55)
| ~ sP16(U_55) )
& ! [U_57,U_58,U_55,U_56] :
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP19(U_57,U_58,U_55,U_56) )
& ! [U_57,U_58,U_55,U_56] :
( ~ aElementOf0(sK7,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP19(U_57,U_58,U_55,U_56) )
& ! [U_57,U_58,U_55,U_56] :
( aElementOf0(sK7,xS)
| ~ sP19(U_57,U_58,U_55,U_56) )
& ! [U_57,U_58,U_55,U_56] :
( aElementOf0(U_58,sdtpldt0(sdtmndt0(xS,xx),xx))
| sP18(U_58)
| ~ aElement0(U_58)
| ~ sP19(U_57,U_58,U_55,U_56) )
& ! [U_57,U_58,U_55,U_56] :
( sP17(U_57)
| ~ aElementOf0(U_57,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP19(U_57,U_58,U_55,U_56) )
& ! [U_57,U_58,U_55,U_56] :
( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP19(U_57,U_58,U_55,U_56) )
& ! [U_57,U_58,U_55,U_56] :
( aElementOf0(U_56,sdtmndt0(xS,xx))
| U_56 = xx
| ~ aElementOf0(U_56,xS)
| ~ aElement0(U_56)
| ~ sP19(U_57,U_58,U_55,U_56) )
& ! [U_57,U_58,U_55,U_56] :
( sP16(U_55)
| ~ aElementOf0(U_55,sdtmndt0(xS,xx))
| ~ sP19(U_57,U_58,U_55,U_56) )
& ! [U_57,U_58,U_55,U_56] :
( aSet0(sdtmndt0(xS,xx))
| ~ sP19(U_57,U_58,U_55,U_56) )
& ! [U_61,U_60,U_57,U_58,U_55,U_62,U_56,U_59] :
( sP23(U_61,U_60,U_62,U_59)
| sP19(U_57,U_58,U_55,U_56) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16,sP17,sP18,sP19,sP20,sP21,sP22,sP23])],[f_19_6]) ).
cnf(f_19_8,negated_conjecture,
( sP23(U_61,U_60,U_62,U_59)
| sP19(U_57,U_58,U_55,U_56) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_9,negated_conjecture,
( aSet0(sdtmndt0(xS,xx))
| ~ sP19(U_57,U_58,U_55,U_56) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_10,negated_conjecture,
( sP16(U_55)
| ~ aElementOf0(U_55,sdtmndt0(xS,xx))
| ~ sP19(U_57,U_58,U_55,U_56) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_11,negated_conjecture,
( aElementOf0(U_56,sdtmndt0(xS,xx))
| U_56 = xx
| ~ aElementOf0(U_56,xS)
| ~ aElement0(U_56)
| ~ sP19(U_57,U_58,U_55,U_56) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_12,negated_conjecture,
( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP19(U_57,U_58,U_55,U_56) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_13,negated_conjecture,
( sP17(U_57)
| ~ aElementOf0(U_57,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP19(U_57,U_58,U_55,U_56) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_14,negated_conjecture,
( aElementOf0(U_58,sdtpldt0(sdtmndt0(xS,xx),xx))
| sP18(U_58)
| ~ aElement0(U_58)
| ~ sP19(U_57,U_58,U_55,U_56) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_15,negated_conjecture,
( aElementOf0(sK7,xS)
| ~ sP19(U_57,U_58,U_55,U_56) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_16,negated_conjecture,
( ~ aElementOf0(sK7,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP19(U_57,U_58,U_55,U_56) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_17,negated_conjecture,
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP19(U_57,U_58,U_55,U_56) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_18,negated_conjecture,
( aElement0(U_55)
| ~ sP16(U_55) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_19,negated_conjecture,
( aElementOf0(U_55,xS)
| ~ sP16(U_55) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_20,negated_conjecture,
( U_55 != xx
| ~ sP16(U_55) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_21,negated_conjecture,
( aElement0(U_57)
| ~ sP17(U_57) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_22,negated_conjecture,
( U_57 = xx
| aElementOf0(U_57,sdtmndt0(xS,xx))
| ~ sP17(U_57) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_23,negated_conjecture,
( ~ aElementOf0(U_58,sdtmndt0(xS,xx))
| ~ sP18(U_58) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_24,negated_conjecture,
( U_58 != xx
| ~ sP18(U_58) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_25,negated_conjecture,
( aSet0(sdtmndt0(xS,xx))
| ~ sP23(U_61,U_60,U_62,U_59) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_26,negated_conjecture,
( sP20(U_59)
| ~ aElementOf0(U_59,sdtmndt0(xS,xx))
| ~ sP23(U_61,U_60,U_62,U_59) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_27,negated_conjecture,
( aElementOf0(U_60,sdtmndt0(xS,xx))
| U_60 = xx
| ~ aElementOf0(U_60,xS)
| ~ aElement0(U_60)
| ~ sP23(U_61,U_60,U_62,U_59) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_28,negated_conjecture,
( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP23(U_61,U_60,U_62,U_59) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_29,negated_conjecture,
( sP21(U_61)
| ~ aElementOf0(U_61,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP23(U_61,U_60,U_62,U_59) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_30,negated_conjecture,
( aElementOf0(U_62,sdtpldt0(sdtmndt0(xS,xx),xx))
| sP22(U_62)
| ~ aElement0(U_62)
| ~ sP23(U_61,U_60,U_62,U_59) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_31,negated_conjecture,
( aElementOf0(sK8,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP23(U_61,U_60,U_62,U_59) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_32,negated_conjecture,
( ~ aElementOf0(sK8,xS)
| ~ sP23(U_61,U_60,U_62,U_59) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_33,negated_conjecture,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ sP23(U_61,U_60,U_62,U_59) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_34,negated_conjecture,
( aElement0(U_59)
| ~ sP20(U_59) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_35,negated_conjecture,
( aElementOf0(U_59,xS)
| ~ sP20(U_59) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_36,negated_conjecture,
( U_59 != xx
| ~ sP20(U_59) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_37,negated_conjecture,
( aElement0(U_61)
| ~ sP21(U_61) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_38,negated_conjecture,
( U_61 = xx
| aElementOf0(U_61,sdtmndt0(xS,xx))
| ~ sP21(U_61) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_39,negated_conjecture,
( ~ aElementOf0(U_62,sdtmndt0(xS,xx))
| ~ sP22(U_62) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_40,negated_conjecture,
( U_62 != xx
| ~ sP22(U_62) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_1_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_5]) ).
cnf(f_2_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_5]) ).
cnf(f_4_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_4]) ).
cnf(f_7_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_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,
( 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_5,axiom,
( sdtmndt0(Eq_x_0,Eq_x_1) = sdtmndt0(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,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_8,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(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_9,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(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_10,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_11,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_12,axiom,
( aSet0(Eq_y_0)
| ~ aSet0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( aElement0(Eq_y_0)
| ~ aElement0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,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_15,axiom,
( isFinite0(Eq_y_0)
| ~ isFinite0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( isCountable0(Eq_y_0)
| ~ isCountable0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( aSubsetOf0(Eq_y_0,Eq_y_1)
| ~ aSubsetOf0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_22,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_25,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_29,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_31,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_34,axiom,
( sP16(Eq_y_0)
| ~ sP16(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP17(Eq_y_0)
| ~ sP17(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP18(Eq_y_0)
| ~ sP18(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_38,axiom,
( sP20(Eq_y_0)
| ~ sP20(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP21(Eq_y_0)
| ~ sP21(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( sP22(Eq_y_0)
| ~ sP22(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM535+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
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 18:44:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 237.96/238.23 % SZS status Theorem for theBenchmark
% 237.96/238.23 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------