TSTP Solution File: NUM534+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM534+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:38:29 EDT 2023
% Result : Theorem 3.30s 3.36s
% Output : CNFRefutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 25
% Syntax : Number of formulae : 195 ( 19 unt; 15 typ; 0 def)
% Number of atoms : 753 ( 136 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 1032 ( 459 ~; 522 |; 35 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 12 >; 9 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 353 ( 20 sgn; 45 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aSet0: $i > $o ).
tff(decl_23,type,
aElement0: $i > $o ).
tff(decl_24,type,
aElementOf0: ( $i * $i ) > $o ).
tff(decl_25,type,
isFinite0: $i > $o ).
tff(decl_26,type,
slcrc0: $i ).
tff(decl_27,type,
isCountable0: $i > $o ).
tff(decl_28,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(decl_29,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_30,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(decl_31,type,
xS: $i ).
tff(decl_32,type,
xx: $i ).
tff(decl_33,type,
esk1_1: $i > $i ).
tff(decl_34,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk4_3: ( $i * $i * $i ) > $i ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDefCons,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtpldt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& ( aElementOf0(X4,X1)
| X4 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).
fof(m__617_02,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617_02) ).
fof(m__617,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__617) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(mSubTrans,axiom,
! [X1,X2,X3] :
( ( aSet0(X1)
& aSet0(X2)
& aSet0(X3) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X2,X3) )
=> aSubsetOf0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(mSubASymm,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubASymm) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& aElementOf0(X4,X1)
& X4 != X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(m__,conjecture,
sdtpldt0(sdtmndt0(xS,xx),xx) = xS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_10,plain,
! [X5,X6] :
( ~ aSet0(X5)
| ~ aElementOf0(X6,X5)
| aElement0(X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_11,plain,
! [X26,X27,X28,X29,X30,X31] :
( ( aSet0(X28)
| X28 != sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( aElement0(X29)
| ~ aElementOf0(X29,X28)
| X28 != sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( aElementOf0(X29,X26)
| X29 = X27
| ~ aElementOf0(X29,X28)
| X28 != sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( ~ aElementOf0(X30,X26)
| ~ aElement0(X30)
| aElementOf0(X30,X28)
| X28 != sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( X30 != X27
| ~ aElement0(X30)
| aElementOf0(X30,X28)
| X28 != sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( ~ aElementOf0(esk3_3(X26,X27,X31),X26)
| ~ aElement0(esk3_3(X26,X27,X31))
| ~ aElementOf0(esk3_3(X26,X27,X31),X31)
| ~ aSet0(X31)
| X31 = sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( esk3_3(X26,X27,X31) != X27
| ~ aElement0(esk3_3(X26,X27,X31))
| ~ aElementOf0(esk3_3(X26,X27,X31),X31)
| ~ aSet0(X31)
| X31 = sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( aElement0(esk3_3(X26,X27,X31))
| aElementOf0(esk3_3(X26,X27,X31),X31)
| ~ aSet0(X31)
| X31 = sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) )
& ( aElementOf0(esk3_3(X26,X27,X31),X26)
| esk3_3(X26,X27,X31) = X27
| aElementOf0(esk3_3(X26,X27,X31),X31)
| ~ aSet0(X31)
| X31 = sdtpldt0(X26,X27)
| ~ aSet0(X26)
| ~ aElement0(X27) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefCons])])])])])]) ).
cnf(c_0_12,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__617_02]) ).
cnf(c_0_14,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__617]) ).
cnf(c_0_15,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aElement0(X1)
| X3 != sdtpldt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( aElementOf0(esk3_3(X1,X2,X3),X1)
| esk3_3(X1,X2,X3) = X2
| aElementOf0(esk3_3(X1,X2,X3),X3)
| X3 = sdtpldt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
fof(c_0_18,plain,
! [X13,X14,X15,X16] :
( ( aSet0(X14)
| ~ aSubsetOf0(X14,X13)
| ~ aSet0(X13) )
& ( ~ aElementOf0(X15,X14)
| aElementOf0(X15,X13)
| ~ aSubsetOf0(X14,X13)
| ~ aSet0(X13) )
& ( aElementOf0(esk2_2(X13,X16),X16)
| ~ aSet0(X16)
| aSubsetOf0(X16,X13)
| ~ aSet0(X13) )
& ( ~ aElementOf0(esk2_2(X13,X16),X13)
| ~ aSet0(X16)
| aSubsetOf0(X16,X13)
| ~ aSet0(X13) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSub])])])])])]) ).
cnf(c_0_19,plain,
( aElementOf0(X1,X2)
| X2 != sdtpldt0(X3,X4)
| ~ aElementOf0(X1,X3)
| ~ aElement0(X4)
| ~ aSet0(X3) ),
inference(csr,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_20,plain,
( aSet0(X1)
| X1 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,hypothesis,
( esk3_3(X1,xx,X2) = xx
| X2 = sdtpldt0(X1,xx)
| aElementOf0(esk3_3(X1,xx,X2),X2)
| aElementOf0(esk3_3(X1,xx,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( aSubsetOf0(X2,X1)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( aElementOf0(X1,sdtpldt0(X2,X3))
| ~ aElementOf0(X1,X2)
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( aSet0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( X3 = sdtpldt0(X1,X2)
| ~ aElementOf0(esk3_3(X1,X2,X3),X1)
| ~ aElement0(esk3_3(X1,X2,X3))
| ~ aElementOf0(esk3_3(X1,X2,X3),X3)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,hypothesis,
( esk3_3(X1,xx,xS) = xx
| sdtpldt0(X1,xx) = xS
| aElementOf0(esk3_3(X1,xx,xS),xS)
| aElementOf0(esk3_3(X1,xx,xS),X1)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_14]) ).
fof(c_0_27,plain,
! [X23,X24,X25] :
( ~ aSet0(X23)
| ~ aSet0(X24)
| ~ aSet0(X25)
| ~ aSubsetOf0(X23,X24)
| ~ aSubsetOf0(X24,X25)
| aSubsetOf0(X23,X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubTrans])]) ).
cnf(c_0_28,plain,
( aSubsetOf0(X1,sdtpldt0(X2,X3))
| ~ aElementOf0(esk2_2(sdtpldt0(X2,X3),X1),X2)
| ~ aElement0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_29,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,plain,
( X1 = sdtpldt0(X2,X3)
| ~ aElementOf0(esk3_3(X2,X3,X1),X1)
| ~ aElementOf0(esk3_3(X2,X3,X1),X2)
| ~ aElement0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[c_0_25,c_0_12]) ).
cnf(c_0_31,hypothesis,
( esk3_3(xS,xx,xS) = xx
| sdtpldt0(xS,xx) = xS
| aElementOf0(esk3_3(xS,xx,xS),xS) ),
inference(spm,[status(thm)],[c_0_26,c_0_14]) ).
cnf(c_0_32,plain,
( aSubsetOf0(X1,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_34,plain,
( X3 = sdtpldt0(X1,X2)
| esk3_3(X1,X2,X3) != X2
| ~ aElement0(esk3_3(X1,X2,X3))
| ~ aElementOf0(esk3_3(X1,X2,X3),X3)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_35,plain,
( aSubsetOf0(X1,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_24]) ).
cnf(c_0_36,hypothesis,
( esk3_3(xS,xx,xS) = xx
| sdtpldt0(xS,xx) = xS ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_17]),c_0_14])]),c_0_31]) ).
cnf(c_0_37,plain,
( aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X3,X2)
| ~ aSubsetOf0(X1,X3)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).
cnf(c_0_38,plain,
( X1 = sdtpldt0(X2,X3)
| esk3_3(X2,X3,X1) != X3
| ~ aElementOf0(esk3_3(X2,X3,X1),X1)
| ~ aElement0(X3)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[c_0_34,c_0_12]) ).
cnf(c_0_39,hypothesis,
( esk3_3(xS,xx,xS) = xx
| aSubsetOf0(xS,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_17]),c_0_14])]) ).
cnf(c_0_40,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_41,plain,
( aSubsetOf0(X1,sdtpldt0(X2,X3))
| ~ aSubsetOf0(X1,X2)
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_35]),c_0_24]) ).
cnf(c_0_42,hypothesis,
( sdtpldt0(xS,xx) = xS
| aSubsetOf0(xS,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_13]),c_0_17]),c_0_14])]) ).
cnf(c_0_43,plain,
( aElementOf0(X1,sdtpldt0(X2,X3))
| ~ aSubsetOf0(X4,X2)
| ~ aElementOf0(X1,X4)
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_24]) ).
cnf(c_0_44,hypothesis,
aSubsetOf0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_42]),c_0_17]),c_0_14])]) ).
cnf(c_0_45,hypothesis,
( aElementOf0(X1,sdtpldt0(xS,X2))
| ~ aElementOf0(X1,xS)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_14])]) ).
cnf(c_0_46,hypothesis,
( aSubsetOf0(X1,sdtpldt0(xS,X2))
| ~ aElementOf0(esk2_2(sdtpldt0(xS,X2),X1),xS)
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(xS,X2))
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_45]) ).
cnf(c_0_47,hypothesis,
( aSubsetOf0(xS,sdtpldt0(xS,X1))
| ~ aElement0(X1)
| ~ aSet0(sdtpldt0(xS,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_29]),c_0_14])]) ).
fof(c_0_48,plain,
! [X21,X22] :
( ~ aSet0(X21)
| ~ aSet0(X22)
| ~ aSubsetOf0(X21,X22)
| ~ aSubsetOf0(X22,X21)
| X21 = X22 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubASymm])]) ).
cnf(c_0_49,hypothesis,
( aSubsetOf0(X1,sdtpldt0(xS,X2))
| ~ aSubsetOf0(X1,xS)
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(xS,X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_47]) ).
cnf(c_0_50,plain,
( aElementOf0(X1,X2)
| X1 = X3
| ~ aElementOf0(X1,X4)
| X4 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_51,plain,
! [X33,X34,X35,X36,X37,X38] :
( ( aSet0(X35)
| X35 != sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( aElement0(X36)
| ~ aElementOf0(X36,X35)
| X35 != sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( aElementOf0(X36,X33)
| ~ aElementOf0(X36,X35)
| X35 != sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( X36 != X34
| ~ aElementOf0(X36,X35)
| X35 != sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( ~ aElement0(X37)
| ~ aElementOf0(X37,X33)
| X37 = X34
| aElementOf0(X37,X35)
| X35 != sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( ~ aElementOf0(esk4_3(X33,X34,X38),X38)
| ~ aElement0(esk4_3(X33,X34,X38))
| ~ aElementOf0(esk4_3(X33,X34,X38),X33)
| esk4_3(X33,X34,X38) = X34
| ~ aSet0(X38)
| X38 = sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( aElement0(esk4_3(X33,X34,X38))
| aElementOf0(esk4_3(X33,X34,X38),X38)
| ~ aSet0(X38)
| X38 = sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( aElementOf0(esk4_3(X33,X34,X38),X33)
| aElementOf0(esk4_3(X33,X34,X38),X38)
| ~ aSet0(X38)
| X38 = sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) )
& ( esk4_3(X33,X34,X38) != X34
| aElementOf0(esk4_3(X33,X34,X38),X38)
| ~ aSet0(X38)
| X38 = sdtmndt0(X33,X34)
| ~ aSet0(X33)
| ~ aElement0(X34) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])])]) ).
cnf(c_0_52,plain,
( X1 = X2
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_53,hypothesis,
( aSet0(X1)
| ~ aSubsetOf0(X1,xS)
| ~ aElement0(X2)
| ~ aSet0(sdtpldt0(xS,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_49]) ).
cnf(c_0_54,plain,
( X1 = X2
| aElementOf0(X1,X3)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_55,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X2)
| X2 != sdtpldt0(X3,X4)
| ~ aSet0(X3)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_56,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_57,plain,
( aSet0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,plain,
( X1 = X2
| ~ aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[c_0_52,c_0_33]) ).
cnf(c_0_59,hypothesis,
( aSet0(X1)
| ~ aSubsetOf0(X1,xS)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_24]),c_0_14])]) ).
cnf(c_0_60,plain,
( esk2_2(X1,sdtpldt0(X2,X3)) = X3
| aSubsetOf0(sdtpldt0(X2,X3),X1)
| aElementOf0(esk2_2(X1,sdtpldt0(X2,X3)),X2)
| ~ aElement0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_29]),c_0_24]) ).
cnf(c_0_61,plain,
( aElement0(X1)
| ~ aElementOf0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_55]) ).
fof(c_0_62,plain,
! [X7,X8,X9] :
( ( aSet0(X7)
| X7 != slcrc0 )
& ( ~ aElementOf0(X8,X7)
| X7 != slcrc0 )
& ( ~ aSet0(X9)
| aElementOf0(esk1_1(X9),X9)
| X9 = slcrc0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefEmp])])])])])]) ).
cnf(c_0_63,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_64,plain,
( aSet0(sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_57]) ).
cnf(c_0_65,hypothesis,
( sdtpldt0(xS,X1) = X2
| ~ aSubsetOf0(sdtpldt0(xS,X1),X2)
| ~ aSubsetOf0(X2,xS)
| ~ aElement0(X1)
| ~ aSet0(sdtpldt0(xS,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_49]),c_0_59]) ).
cnf(c_0_66,plain,
( esk2_2(X1,sdtpldt0(X1,X2)) = X2
| aSubsetOf0(sdtpldt0(X1,X2),X1)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_60]),c_0_24]) ).
cnf(c_0_67,hypothesis,
( aElement0(X1)
| ~ aElementOf0(X1,xS)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_45]),c_0_14])]) ).
cnf(c_0_68,plain,
( ~ aElementOf0(X1,X2)
| X2 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_69,plain,
( aSubsetOf0(sdtmndt0(X1,X2),X3)
| aElementOf0(esk2_2(X3,sdtmndt0(X1,X2)),X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| ~ aSet0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_29]),c_0_64]) ).
cnf(c_0_70,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,hypothesis,
( sdtpldt0(xS,X1) = sdtpldt0(xS,X2)
| ~ aSubsetOf0(sdtpldt0(xS,X2),xS)
| ~ aSubsetOf0(sdtpldt0(xS,X1),xS)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_49]),c_0_59]),c_0_59]) ).
cnf(c_0_72,plain,
( aSubsetOf0(sdtpldt0(X1,X2),X1)
| ~ aElementOf0(X2,X1)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_66]),c_0_24]),c_0_12]) ).
cnf(c_0_73,hypothesis,
( aElement0(X1)
| ~ aElementOf0(X1,xS) ),
inference(spm,[status(thm)],[c_0_67,c_0_17]) ).
cnf(c_0_74,plain,
( aSubsetOf0(sdtmndt0(X1,X2),X3)
| X1 != slcrc0
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_75,plain,
( aElementOf0(esk1_1(X1),X1)
| X1 = slcrc0
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_76,hypothesis,
( sdtpldt0(xS,X1) = sdtpldt0(xS,X2)
| ~ aSubsetOf0(sdtpldt0(xS,X1),xS)
| ~ aElementOf0(X2,xS)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_14])]),c_0_73]) ).
cnf(c_0_77,plain,
( aSet0(sdtmndt0(X1,X2))
| X1 != slcrc0
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_74]) ).
cnf(c_0_78,plain,
( sdtmndt0(X1,X2) = slcrc0
| aElementOf0(esk1_1(sdtmndt0(X1,X2)),X1)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_75]),c_0_64]) ).
cnf(c_0_79,hypothesis,
( sdtpldt0(xS,X1) = sdtpldt0(xS,X2)
| ~ aElementOf0(X2,xS)
| ~ aElementOf0(X1,xS) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_72]),c_0_14])]),c_0_73]) ).
cnf(c_0_80,plain,
( aElementOf0(esk4_3(X1,X2,X3),X1)
| aElementOf0(esk4_3(X1,X2,X3),X3)
| X3 = sdtmndt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_81,hypothesis,
( aSet0(sdtmndt0(X1,X2))
| X1 != slcrc0
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_14]) ).
cnf(c_0_82,plain,
( sdtmndt0(X1,X2) = slcrc0
| X1 != slcrc0
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_78]),c_0_70]) ).
cnf(c_0_83,plain,
( aSubsetOf0(X1,sdtpldt0(X2,X3))
| ~ aSubsetOf0(X1,X4)
| ~ aSubsetOf0(X4,X2)
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_41]),c_0_24]) ).
cnf(c_0_84,plain,
( aSubsetOf0(sdtmndt0(X1,X2),sdtpldt0(X1,X3))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_69]),c_0_24]),c_0_64]) ).
cnf(c_0_85,hypothesis,
( aSubsetOf0(sdtpldt0(xS,X1),xS)
| ~ aElementOf0(X2,xS)
| ~ aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_79]),c_0_14])]) ).
cnf(c_0_86,hypothesis,
xS != slcrc0,
inference(spm,[status(thm)],[c_0_68,c_0_13]) ).
cnf(c_0_87,plain,
( aSubsetOf0(sdtmndt0(X1,X2),X1)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_69]),c_0_64]) ).
cnf(c_0_88,hypothesis,
( X1 = sdtmndt0(X2,xx)
| aElementOf0(esk4_3(X2,xx,X1),X1)
| aElementOf0(esk4_3(X2,xx,X1),X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_17]) ).
cnf(c_0_89,hypothesis,
( aSet0(slcrc0)
| X1 != slcrc0
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_90,plain,
( aSubsetOf0(sdtmndt0(X1,X2),sdtpldt0(X3,X4))
| ~ aSubsetOf0(sdtpldt0(X1,X5),X3)
| ~ aElement0(X4)
| ~ aElement0(X5)
| ~ aElement0(X2)
| ~ aSet0(X3)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_91,hypothesis,
( aSubsetOf0(sdtpldt0(xS,X1),xS)
| ~ aElementOf0(X1,xS) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_75]),c_0_14])]),c_0_86]) ).
cnf(c_0_92,plain,
( aSubsetOf0(X1,X2)
| X1 != slcrc0
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_29]),c_0_70]) ).
cnf(c_0_93,plain,
( aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X1,sdtmndt0(X2,X3))
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_87]) ).
cnf(c_0_94,hypothesis,
( X1 = sdtmndt0(X2,xx)
| aElementOf0(esk4_3(X2,xx,X1),X2)
| X1 != slcrc0
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_70]),c_0_68]) ).
cnf(c_0_95,hypothesis,
( aSet0(slcrc0)
| X1 != slcrc0 ),
inference(spm,[status(thm)],[c_0_89,c_0_17]) ).
cnf(c_0_96,hypothesis,
( aSubsetOf0(sdtmndt0(xS,X1),sdtpldt0(xS,X2))
| ~ aElementOf0(X3,xS)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_14])]),c_0_73]) ).
cnf(c_0_97,plain,
( X1 = X2
| X2 != slcrc0
| ~ aSubsetOf0(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_92]),c_0_33]),c_0_70]) ).
cnf(c_0_98,plain,
( aSubsetOf0(sdtmndt0(sdtmndt0(X1,X2),X3),X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_87]),c_0_64]) ).
cnf(c_0_99,hypothesis,
( X1 = sdtmndt0(X2,xx)
| X2 != slcrc0
| X1 != slcrc0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_94]),c_0_70]) ).
cnf(c_0_100,hypothesis,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_95]) ).
cnf(c_0_101,hypothesis,
( aSubsetOf0(sdtmndt0(xS,X1),sdtpldt0(xS,X2))
| aSubsetOf0(xS,X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aSet0(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_29]),c_0_14])]) ).
cnf(c_0_102,plain,
( X1 != X2
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X4,X2)
| ~ aSet0(X4)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_103,plain,
( sdtmndt0(sdtmndt0(X1,X2),X3) = X1
| X1 != slcrc0
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_70]) ).
cnf(c_0_104,hypothesis,
( sdtmndt0(X1,xx) = slcrc0
| X1 != slcrc0 ),
inference(er,[status(thm)],[c_0_99]) ).
cnf(c_0_105,hypothesis,
( sdtmndt0(X1,xx) = xS
| aElementOf0(esk4_3(X1,xx,xS),xS)
| aElementOf0(esk4_3(X1,xx,xS),X1)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_14]) ).
cnf(c_0_106,hypothesis,
( sdtmndt0(X1,xx) = slcrc0
| aElementOf0(esk4_3(X1,xx,slcrc0),slcrc0)
| aElementOf0(esk4_3(X1,xx,slcrc0),X1)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_100]) ).
cnf(c_0_107,hypothesis,
( aSubsetOf0(sdtmndt0(xS,X1),sdtpldt0(xS,xx))
| aSubsetOf0(xS,X2)
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(spm,[status(thm)],[c_0_101,c_0_17]) ).
cnf(c_0_108,hypothesis,
( aSubsetOf0(xS,sdtpldt0(xS,X1))
| ~ aElementOf0(X2,xS)
| ~ aElementOf0(X1,xS) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_79]),c_0_14])]),c_0_73]) ).
cnf(c_0_109,hypothesis,
( aSet0(sdtpldt0(xS,X1))
| ~ aElementOf0(X1,xS)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_72]),c_0_14])]) ).
cnf(c_0_110,plain,
( X1 != sdtmndt0(X2,X3)
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_102]) ).
cnf(c_0_111,hypothesis,
( sdtmndt0(slcrc0,X1) = X2
| X2 != slcrc0
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_17])]) ).
cnf(c_0_112,hypothesis,
( sdtmndt0(sdtmndt0(X1,X2),xx) = xS
| aElementOf0(esk4_3(sdtmndt0(X1,X2),xx,xS),sdtmndt0(X1,X2))
| aElementOf0(esk4_3(sdtmndt0(X1,X2),xx,xS),xS)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_64]) ).
cnf(c_0_113,hypothesis,
( sdtmndt0(slcrc0,xx) = slcrc0
| aElementOf0(esk4_3(slcrc0,xx,slcrc0),slcrc0) ),
inference(spm,[status(thm)],[c_0_106,c_0_100]) ).
cnf(c_0_114,hypothesis,
( aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(xS,xx))
| aSubsetOf0(xS,X1)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_17]) ).
cnf(c_0_115,hypothesis,
( aSubsetOf0(xS,sdtpldt0(xS,X1))
| ~ aElementOf0(X1,xS) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_75]),c_0_14])]),c_0_86]) ).
cnf(c_0_116,hypothesis,
( aSet0(sdtpldt0(xS,X1))
| ~ aElementOf0(X1,xS) ),
inference(spm,[status(thm)],[c_0_109,c_0_17]) ).
cnf(c_0_117,plain,
( ~ aElementOf0(X1,sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_110]) ).
cnf(c_0_118,hypothesis,
( sdtmndt0(slcrc0,X1) = slcrc0
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_111]) ).
cnf(c_0_119,hypothesis,
( sdtmndt0(sdtmndt0(X1,X2),xx) = xS
| aElement0(esk4_3(sdtmndt0(X1,X2),xx,xS))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_112]),c_0_64]),c_0_73]) ).
cnf(c_0_120,hypothesis,
sdtmndt0(slcrc0,xx) = slcrc0,
inference(spm,[status(thm)],[c_0_68,c_0_113]) ).
cnf(c_0_121,hypothesis,
( aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(xS,xx))
| aSubsetOf0(xS,sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_64]) ).
cnf(c_0_122,plain,
( aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X1,sdtpldt0(X2,X3))
| ~ aElementOf0(X3,X2)
| ~ aSet0(X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_72]) ).
cnf(c_0_123,plain,
( aSet0(sdtpldt0(X1,X2))
| ~ aElementOf0(X2,X1)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_72]) ).
cnf(c_0_124,hypothesis,
( aSubsetOf0(X1,sdtpldt0(xS,X2))
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X2,xS) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_115]),c_0_116]) ).
cnf(c_0_125,hypothesis,
( ~ aElementOf0(X1,slcrc0)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_100])]) ).
cnf(c_0_126,hypothesis,
aElement0(esk4_3(slcrc0,xx,xS)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_120]),c_0_17]),c_0_100])]),c_0_86]) ).
cnf(c_0_127,hypothesis,
( aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(xS,xx))
| aSubsetOf0(xS,sdtmndt0(X1,xx))
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_17]) ).
cnf(c_0_128,plain,
( aSubsetOf0(sdtmndt0(sdtpldt0(X1,X2),X3),X1)
| ~ aElementOf0(X2,X1)
| ~ aElement0(X3)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_87]),c_0_123]) ).
cnf(c_0_129,hypothesis,
( aSet0(X1)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X2,xS) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_124]),c_0_116]) ).
cnf(c_0_130,hypothesis,
( sdtmndt0(slcrc0,xx) = xS
| aElementOf0(esk4_3(slcrc0,xx,xS),slcrc0)
| aElementOf0(esk4_3(slcrc0,xx,xS),xS) ),
inference(spm,[status(thm)],[c_0_105,c_0_100]) ).
cnf(c_0_131,hypothesis,
~ aElementOf0(esk4_3(slcrc0,xx,xS),slcrc0),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_132,hypothesis,
( aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(xS,xx))
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(X1,X2),xx))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_127,c_0_24]) ).
cnf(c_0_133,hypothesis,
( aSubsetOf0(sdtmndt0(sdtpldt0(xS,X1),X2),xS)
| ~ aElementOf0(X3,xS)
| ~ aElementOf0(X1,xS)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_79]),c_0_14])]) ).
cnf(c_0_134,hypothesis,
( aSet0(sdtmndt0(sdtpldt0(xS,X1),X2))
| ~ aElementOf0(X3,xS)
| ~ aElementOf0(X1,xS)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_128]),c_0_14])]) ).
cnf(c_0_135,hypothesis,
aElementOf0(esk4_3(slcrc0,xx,xS),xS),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_120]),c_0_86]),c_0_131]) ).
cnf(c_0_136,hypothesis,
( aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(xS,xx))
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(X1,xx),xx))
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_132,c_0_17]) ).
cnf(c_0_137,plain,
( sdtpldt0(X1,X2) = X3
| ~ aSubsetOf0(sdtpldt0(X1,X2),X3)
| ~ aSubsetOf0(X3,X1)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_41]),c_0_33]) ).
cnf(c_0_138,hypothesis,
( aSubsetOf0(sdtmndt0(sdtpldt0(xS,X1),X2),xS)
| ~ aElementOf0(X1,xS)
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[c_0_133,c_0_13]) ).
cnf(c_0_139,hypothesis,
( aSet0(sdtmndt0(sdtpldt0(xS,X1),X2))
| ~ aElementOf0(X1,xS)
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_140,hypothesis,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(xS,xx)) ),
inference(spm,[status(thm)],[c_0_136,c_0_14]) ).
cnf(c_0_141,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X3,X4)
| ~ aSubsetOf0(sdtpldt0(X3,X4),X1)
| ~ aSubsetOf0(sdtpldt0(X1,X2),X3)
| ~ aElement0(X2)
| ~ aElement0(X4)
| ~ aSet0(X1)
| ~ aSet0(X3) ),
inference(spm,[status(thm)],[c_0_137,c_0_41]) ).
cnf(c_0_142,hypothesis,
( aSet0(sdtmndt0(xS,X1))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_87]),c_0_14])]) ).
cnf(c_0_143,hypothesis,
( sdtmndt0(sdtpldt0(xS,X1),X2) = xS
| ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,X1),X2))
| ~ aElementOf0(X1,xS)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_138]),c_0_139]) ).
cnf(c_0_144,hypothesis,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| aSubsetOf0(sdtmndt0(xS,xx),xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_140]),c_0_13]),c_0_14])]) ).
cnf(c_0_145,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| ~ aSubsetOf0(sdtpldt0(X1,X2),X1)
| ~ aElementOf0(X3,X1)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_72]),c_0_12]) ).
cnf(c_0_146,hypothesis,
( aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X1,sdtpldt0(xS,X2))
| ~ aElementOf0(X2,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_91]),c_0_14])]) ).
cnf(c_0_147,plain,
( aSubsetOf0(sdtmndt0(X1,X2),sdtpldt0(X3,X4))
| ~ aSubsetOf0(X1,X3)
| ~ aElement0(X4)
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_87]),c_0_33]) ).
cnf(c_0_148,hypothesis,
( aSet0(sdtmndt0(xS,X1))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_142,c_0_17]) ).
cnf(c_0_149,hypothesis,
( sdtmndt0(sdtpldt0(xS,xx),xx) = xS
| aSubsetOf0(sdtmndt0(xS,xx),xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_13]),c_0_17])]) ).
cnf(c_0_150,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X2,X1)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_72]),c_0_12]) ).
cnf(c_0_151,hypothesis,
( aSubsetOf0(sdtmndt0(X1,X2),xS)
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X3,xS)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_14])]),c_0_73]) ).
cnf(c_0_152,hypothesis,
( aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(xS,xx))
| aSubsetOf0(xS,sdtmndt0(xS,X1))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_148]) ).
cnf(c_0_153,hypothesis,
( sdtpldt0(xS,X1) = xS
| ~ aSubsetOf0(sdtpldt0(xS,X1),xS)
| ~ aElement0(X1)
| ~ aSet0(sdtpldt0(xS,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_47]),c_0_14])]) ).
cnf(c_0_154,hypothesis,
( sdtmndt0(sdtpldt0(xS,X1),xx) = xS
| aSubsetOf0(sdtmndt0(xS,xx),xS)
| ~ aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_13]),c_0_14])]) ).
cnf(c_0_155,hypothesis,
( aSubsetOf0(sdtmndt0(X1,X2),xS)
| ~ aSubsetOf0(X1,xS)
| ~ aElement0(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_75]),c_0_14])]),c_0_86]) ).
cnf(c_0_156,hypothesis,
( aSubsetOf0(sdtmndt0(xS,xx),sdtpldt0(xS,xx))
| aSubsetOf0(xS,sdtmndt0(xS,xx)) ),
inference(spm,[status(thm)],[c_0_152,c_0_17]) ).
cnf(c_0_157,hypothesis,
( sdtpldt0(xS,X1) = xS
| ~ aElementOf0(X1,xS) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_72]),c_0_14])]),c_0_109]),c_0_73]) ).
cnf(c_0_158,hypothesis,
( aSubsetOf0(sdtmndt0(xS,xx),xS)
| ~ aElementOf0(X1,xS) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_154]),c_0_13]),c_0_17])]),c_0_116]) ).
cnf(c_0_159,plain,
( sdtpldt0(X1,X2) = sdtmndt0(X3,X4)
| ~ aSubsetOf0(sdtpldt0(X1,X2),sdtmndt0(X3,X4))
| ~ aSubsetOf0(X3,X1)
| ~ aElement0(X2)
| ~ aElement0(X4)
| ~ aSet0(sdtmndt0(X3,X4))
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_147]) ).
cnf(c_0_160,hypothesis,
( aSet0(sdtmndt0(X1,X2))
| ~ aSubsetOf0(X1,xS)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_155]),c_0_14])]) ).
cnf(c_0_161,hypothesis,
( aSubsetOf0(xS,sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_156]),c_0_13]),c_0_14])]) ).
cnf(c_0_162,hypothesis,
( aSet0(X1)
| X1 != xS
| ~ aElementOf0(X2,xS) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_157]),c_0_14])]),c_0_73]) ).
cnf(c_0_163,hypothesis,
aSubsetOf0(sdtmndt0(xS,xx),xS),
inference(spm,[status(thm)],[c_0_158,c_0_135]) ).
fof(c_0_164,negated_conjecture,
sdtpldt0(sdtmndt0(xS,xx),xx) != xS,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_165,hypothesis,
( sdtmndt0(X1,X2) = xS
| ~ aSubsetOf0(xS,sdtmndt0(X1,X2))
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X3,xS)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_157]),c_0_14])]),c_0_160]),c_0_73]) ).
cnf(c_0_166,hypothesis,
( aSubsetOf0(xS,sdtmndt0(xS,xx))
| aSet0(sdtmndt0(xS,xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_161]),c_0_14])]) ).
cnf(c_0_167,hypothesis,
( aSet0(X1)
| X1 != xS ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_75]),c_0_14])]),c_0_86]) ).
cnf(c_0_168,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtmndt0(xS,xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_163]),c_0_14])]) ).
cnf(c_0_169,hypothesis,
( esk3_3(sdtmndt0(X1,X2),xx,xS) = xx
| sdtpldt0(sdtmndt0(X1,X2),xx) = xS
| aElementOf0(esk3_3(sdtmndt0(X1,X2),xx,xS),sdtmndt0(X1,X2))
| aElementOf0(esk3_3(sdtmndt0(X1,X2),xx,xS),xS)
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_64]) ).
cnf(c_0_170,negated_conjecture,
sdtpldt0(sdtmndt0(xS,xx),xx) != xS,
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_171,hypothesis,
( aSet0(sdtmndt0(xS,xx))
| ~ aElementOf0(X1,xS) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_44]),c_0_17])]),c_0_167]) ).
cnf(c_0_172,plain,
( X1 = X3
| aElementOf0(X1,X4)
| ~ aElement0(X1)
| ~ aElementOf0(X1,X2)
| X4 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_173,hypothesis,
( esk3_3(sdtmndt0(xS,xx),xx,xS) = xx
| aElementOf0(esk3_3(sdtmndt0(xS,xx),xx,xS),xS) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_17]),c_0_14])]),c_0_170]) ).
cnf(c_0_174,hypothesis,
aSet0(sdtmndt0(xS,xx)),
inference(spm,[status(thm)],[c_0_171,c_0_135]) ).
cnf(c_0_175,plain,
( X1 = X2
| aElementOf0(X1,X3)
| X3 != sdtmndt0(X4,X2)
| ~ aElementOf0(X1,X4)
| ~ aElement0(X2)
| ~ aSet0(X4) ),
inference(csr,[status(thm)],[c_0_172,c_0_12]) ).
cnf(c_0_176,hypothesis,
( esk3_3(sdtmndt0(xS,xx),xx,xS) = xx
| ~ aElementOf0(esk3_3(sdtmndt0(xS,xx),xx,xS),sdtmndt0(xS,xx)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_173]),c_0_17]),c_0_14]),c_0_174])]),c_0_170]) ).
cnf(c_0_177,plain,
( X1 = X2
| aElementOf0(X1,sdtmndt0(X3,X2))
| ~ aElementOf0(X1,X3)
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_175]) ).
cnf(c_0_178,hypothesis,
esk3_3(sdtmndt0(xS,xx),xx,xS) = xx,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_17]),c_0_14])]),c_0_173]) ).
cnf(c_0_179,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_178]),c_0_13]),c_0_17]),c_0_14]),c_0_174])]),c_0_170]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM534+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 16:07:02 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.21/0.63 start to proof: theBenchmark
% 3.30/3.36 % Version : CSE_E---1.5
% 3.30/3.36 % Problem : theBenchmark.p
% 3.30/3.36 % Proof found
% 3.30/3.36 % SZS status Theorem for theBenchmark.p
% 3.30/3.36 % SZS output start Proof
% See solution above
% 3.30/3.37 % Total time : 2.715000 s
% 3.30/3.37 % SZS output end Proof
% 3.30/3.37 % Total time : 2.718000 s
%------------------------------------------------------------------------------