%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM554+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:57:48 PM UTC 2026
% Result : Theorem 4.19s 3.21s
% Output : CNFRefutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 97 ( 34 unt; 0 def)
% Number of atoms : 424 ( 81 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 557 ( 230 ~; 249 |; 48 &)
% ( 7 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 133 ( 0 sgn 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDiffCons,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aSet0(X2) )
=> ( ~ aElementOf0(X1,X2)
=> sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2256,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
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/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(mFConsSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( aSet0(X2)
& isFinite0(X2) )
=> isFinite0(sdtpldt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).
fof(m__2357,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
fof(mFDiffSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( aSet0(X2)
& isFinite0(X2) )
=> isFinite0(sdtmndt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
fof(mCardCons,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardCons) ).
fof(m__2304,hypothesis,
( aElement0(xy)
& aElementOf0(xy,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
fof(m__2291,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(m__2323,hypothesis,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2323) ).
fof(mDefSel,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElementOf0(X2,szNzAzT0) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aSubsetOf0(X4,X1)
& sbrdtbr0(X4) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(mCardDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( ( isFinite0(X1)
& aElementOf0(X2,X1) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(m__,conjecture,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2202,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).
fof(m__2270,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
fof(c_0_19,plain,
! [X1,X2] :
( ( aElement0(X1)
& aSet0(X2) )
=> ( ~ aElementOf0(X1,X2)
=> sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
inference(fof_simplification,[status(thm)],[mDiffCons]) ).
fof(c_0_20,plain,
! [X111,X112] :
( ~ aSet0(X111)
| ~ aElementOf0(X112,X111)
| aElement0(X112) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_21,plain,
! [X148,X149] :
( ~ aElement0(X148)
| ~ aSet0(X149)
| aElementOf0(X148,X149)
| sdtmndt0(sdtpldt0(X149,X148),X148) = X149 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).
cnf(c_0_22,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__2256]) ).
cnf(c_0_24,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__2202_02]) ).
fof(c_0_25,plain,
! [X139,X140,X141,X142,X143,X144] :
( ( aSet0(X141)
| X141 != sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( aElement0(X142)
| ~ aElementOf0(X142,X141)
| X141 != sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( aElementOf0(X142,X139)
| ~ aElementOf0(X142,X141)
| X141 != sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( X142 != X140
| ~ aElementOf0(X142,X141)
| X141 != sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( ~ aElement0(X143)
| ~ aElementOf0(X143,X139)
| X143 = X140
| aElementOf0(X143,X141)
| X141 != sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( ~ aElementOf0(esk4_3(X139,X140,X144),X144)
| ~ aElement0(esk4_3(X139,X140,X144))
| ~ aElementOf0(esk4_3(X139,X140,X144),X139)
| esk4_3(X139,X140,X144) = X140
| ~ aSet0(X144)
| X144 = sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( aElement0(esk4_3(X139,X140,X144))
| aElementOf0(esk4_3(X139,X140,X144),X144)
| ~ aSet0(X144)
| X144 = sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( aElementOf0(esk4_3(X139,X140,X144),X139)
| aElementOf0(esk4_3(X139,X140,X144),X144)
| ~ aSet0(X144)
| X144 = sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) )
& ( esk4_3(X139,X140,X144) != X140
| aElementOf0(esk4_3(X139,X140,X144),X144)
| ~ aSet0(X144)
| X144 = sdtmndt0(X139,X140)
| ~ aSet0(X139)
| ~ aElement0(X140) ) ),
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])])])])])]) ).
fof(c_0_26,plain,
! [X132,X133,X134,X135,X136,X137] :
( ( aSet0(X134)
| X134 != sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( aElement0(X135)
| ~ aElementOf0(X135,X134)
| X134 != sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( aElementOf0(X135,X132)
| X135 = X133
| ~ aElementOf0(X135,X134)
| X134 != sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( ~ aElementOf0(X136,X132)
| ~ aElement0(X136)
| aElementOf0(X136,X134)
| X134 != sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( X136 != X133
| ~ aElement0(X136)
| aElementOf0(X136,X134)
| X134 != sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( ~ aElementOf0(esk3_3(X132,X133,X137),X132)
| ~ aElement0(esk3_3(X132,X133,X137))
| ~ aElementOf0(esk3_3(X132,X133,X137),X137)
| ~ aSet0(X137)
| X137 = sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( esk3_3(X132,X133,X137) != X133
| ~ aElement0(esk3_3(X132,X133,X137))
| ~ aElementOf0(esk3_3(X132,X133,X137),X137)
| ~ aSet0(X137)
| X137 = sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( aElement0(esk3_3(X132,X133,X137))
| aElementOf0(esk3_3(X132,X133,X137),X137)
| ~ aSet0(X137)
| X137 = sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) )
& ( aElementOf0(esk3_3(X132,X133,X137),X132)
| esk3_3(X132,X133,X137) = X133
| aElementOf0(esk3_3(X132,X133,X137),X137)
| ~ aSet0(X137)
| X137 = sdtpldt0(X132,X133)
| ~ aSet0(X132)
| ~ aElement0(X133) ) ),
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])])])])])]) ).
fof(c_0_27,plain,
! [X154,X155] :
( ~ aElement0(X154)
| ~ aSet0(X155)
| ~ isFinite0(X155)
| isFinite0(sdtpldt0(X155,X154)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFConsSet])])]) ).
cnf(c_0_28,plain,
( aElementOf0(X1,X2)
| sdtmndt0(sdtpldt0(X2,X1),X1) = X2
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(split_conjunct,[status(thm)],[m__2357]) ).
cnf(c_0_30,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_31,plain,
( aSet0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( aSet0(X1)
| X1 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( isFinite0(sdtpldt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_34,plain,
! [X156,X157] :
( ~ aElement0(X156)
| ~ aSet0(X157)
| ~ isFinite0(X157)
| isFinite0(sdtmndt0(X157,X156)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFDiffSet])])]) ).
fof(c_0_35,plain,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[mCardCons]) ).
cnf(c_0_36,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,hypothesis,
( sdtmndt0(xP,xx) = sdtmndt0(xQ,xy)
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_38,plain,
( aSet0(sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_39,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_40,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
fof(c_0_41,hypothesis,
~ aElementOf0(xx,xQ),
inference(fof_simplification,[status(thm)],[m__2323]) ).
cnf(c_0_42,plain,
( aSet0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_43,hypothesis,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_29]),c_0_30])]) ).
cnf(c_0_44,plain,
( isFinite0(sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,hypothesis,
isFinite0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
fof(c_0_46,plain,
! [X181,X182] :
( ~ aSet0(X181)
| ~ isFinite0(X181)
| ~ aElement0(X182)
| aElementOf0(X182,X181)
| sbrdtbr0(sdtpldt0(X181,X182)) = szszuzczcdt0(sbrdtbr0(X181)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
cnf(c_0_47,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_48,hypothesis,
( sdtmndt0(xP,xx) = sdtmndt0(xQ,xy)
| aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40])]) ).
cnf(c_0_49,hypothesis,
~ aElementOf0(xx,xQ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,hypothesis,
( aSet0(xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_29]),c_0_30])]) ).
cnf(c_0_51,plain,
( X1 != X2
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X4,X2)
| ~ aSet0(X4)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_52,hypothesis,
( isFinite0(xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_39]),c_0_40])]) ).
cnf(c_0_53,plain,
( aElementOf0(X2,X1)
| sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1))
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,hypothesis,
sdtmndt0(xP,xx) = sdtmndt0(xQ,xy),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_39]),c_0_40])]),c_0_49]) ).
cnf(c_0_55,hypothesis,
aSet0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_38]),c_0_39]),c_0_40])]) ).
cnf(c_0_56,plain,
( ~ aElementOf0(X1,sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_51])]) ).
cnf(c_0_57,hypothesis,
isFinite0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_38]),c_0_39]),c_0_40])]) ).
fof(c_0_58,plain,
! [X216,X217,X218,X219,X220,X221] :
( ( aSet0(X218)
| X218 != slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( aSubsetOf0(X219,X216)
| ~ aElementOf0(X219,X218)
| X218 != slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( sbrdtbr0(X219) = X217
| ~ aElementOf0(X219,X218)
| X218 != slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( ~ aSubsetOf0(X220,X216)
| sbrdtbr0(X220) != X217
| aElementOf0(X220,X218)
| X218 != slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( ~ aElementOf0(esk11_3(X216,X217,X221),X221)
| ~ aSubsetOf0(esk11_3(X216,X217,X221),X216)
| sbrdtbr0(esk11_3(X216,X217,X221)) != X217
| ~ aSet0(X221)
| X221 = slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( aSubsetOf0(esk11_3(X216,X217,X221),X216)
| aElementOf0(esk11_3(X216,X217,X221),X221)
| ~ aSet0(X221)
| X221 = slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) )
& ( sbrdtbr0(esk11_3(X216,X217,X221)) = X217
| aElementOf0(esk11_3(X216,X217,X221),X221)
| ~ aSet0(X221)
| X221 = slbdtsldtrb0(X216,X217)
| ~ aSet0(X216)
| ~ aElementOf0(X217,szNzAzT0) ) ),
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)],[mDefSel])])])])])]) ).
fof(c_0_59,plain,
! [X183,X184] :
( ~ aSet0(X183)
| ~ isFinite0(X183)
| ~ aElementOf0(X184,X183)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X183,X184))) = sbrdtbr0(X183) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardDiff])])]) ).
cnf(c_0_60,hypothesis,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xP)
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_29]),c_0_30])]) ).
cnf(c_0_61,hypothesis,
aSet0(sdtmndt0(xQ,xy)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_54]),c_0_30]),c_0_55])]) ).
cnf(c_0_62,hypothesis,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_54]),c_0_30]),c_0_55])]) ).
cnf(c_0_63,hypothesis,
isFinite0(sdtmndt0(xQ,xy)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_54]),c_0_57]),c_0_30]),c_0_55])]) ).
fof(c_0_64,plain,
! [X119,X120,X121,X122] :
( ( aSet0(X120)
| ~ aSubsetOf0(X120,X119)
| ~ aSet0(X119) )
& ( ~ aElementOf0(X121,X120)
| aElementOf0(X121,X119)
| ~ aSubsetOf0(X120,X119)
| ~ aSet0(X119) )
& ( aElementOf0(esk2_2(X119,X122),X122)
| ~ aSet0(X122)
| aSubsetOf0(X122,X119)
| ~ aSet0(X119) )
& ( ~ aElementOf0(esk2_2(X119,X122),X119)
| ~ aSet0(X122)
| aSubsetOf0(X122,X119)
| ~ aSet0(X119) ) ),
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_65,plain,
( aElementOf0(X1,X4)
| ~ aSubsetOf0(X1,X2)
| sbrdtbr0(X1) != X3
| X4 != slbdtsldtrb0(X2,X3)
| ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_66,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_67,hypothesis,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]),c_0_62]),c_0_63])]) ).
cnf(c_0_68,hypothesis,
sbrdtbr0(xQ) = xk,
inference(split_conjunct,[status(thm)],[m__2291]) ).
cnf(c_0_69,hypothesis,
aElementOf0(xy,xQ),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_70,plain,
( aElementOf0(X1,X2)
| X1 = X3
| ~ aElementOf0(X1,X4)
| X4 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_71,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_72,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_73,plain,
( aElementOf0(X1,slbdtsldtrb0(X2,sbrdtbr0(X1)))
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_65])]) ).
cnf(c_0_74,hypothesis,
sbrdtbr0(xP) = xk,
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_66,c_0_67]),c_0_68]),c_0_45]),c_0_69]),c_0_40])]) ).
cnf(c_0_75,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__2202]) ).
cnf(c_0_76,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aSet0(X2)
| ~ aElementOf0(X4,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_77,plain,
( X1 = X2
| aElementOf0(X1,X3)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_70]) ).
cnf(c_0_78,hypothesis,
( aSubsetOf0(xP,X1)
| aElementOf0(esk2_2(X1,xP),xP)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_55]) ).
cnf(c_0_79,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_80,hypothesis,
( aElementOf0(xP,slbdtsldtrb0(X1,xk))
| ~ aSubsetOf0(xP,X1)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_81,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_76]) ).
cnf(c_0_82,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[m__2270]) ).
cnf(c_0_83,hypothesis,
( X1 = xx
| aElementOf0(X1,sdtmndt0(xQ,xy))
| ~ aElementOf0(X1,xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_29]),c_0_30])]) ).
cnf(c_0_84,hypothesis,
( aSubsetOf0(xP,xS)
| aElementOf0(esk2_2(xS,xP),xP) ),
inference(spm,[status(thm)],[c_0_78,c_0_24]) ).
cnf(c_0_85,negated_conjecture,
~ aSubsetOf0(xP,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_24])]) ).
cnf(c_0_86,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_87,hypothesis,
aSubsetOf0(xQ,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_75]),c_0_24])]) ).
cnf(c_0_88,hypothesis,
( X1 = xx
| aElementOf0(X1,sdtmndt0(xQ,xy))
| ~ aElementOf0(X1,xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_61])]) ).
cnf(c_0_89,hypothesis,
aElementOf0(esk2_2(xS,xP),xP),
inference(sr,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,plain,
( aSubsetOf0(X2,X1)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_91,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_24])]) ).
cnf(c_0_92,hypothesis,
( esk2_2(xS,xP) = xx
| aElementOf0(esk2_2(xS,xP),sdtmndt0(xQ,xy)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_93,hypothesis,
( aSubsetOf0(X1,xS)
| ~ aElementOf0(esk2_2(xS,X1),xQ)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_24])]) ).
cnf(c_0_94,hypothesis,
( esk2_2(xS,xP) = xx
| aElementOf0(esk2_2(xS,xP),xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_92]),c_0_39]),c_0_40])]) ).
cnf(c_0_95,hypothesis,
esk2_2(xS,xP) = xx,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_55])]),c_0_85]) ).
cnf(c_0_96,hypothesis,
$false,
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_90,c_0_95]),c_0_23]),c_0_55]),c_0_24])]),c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM554+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n023.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:44:53 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.19/3.21 % Version : CSE_E---1.7
% 4.19/3.21 % Problem : theBenchmark.p
% 4.19/3.21 % SZS status Theorem for theBenchmark.p
% 4.19/3.21 % SZS output start CNFRefutation
% See solution above
% 4.19/3.22 % Total time : 2.374s
%------------------------------------------------------------------------------