%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM596+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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:57:58 PM UTC 2026
% Result : Theorem 6.78s 4.64s
% Output : CNFRefutation 6.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 61 ( 17 unt; 0 def)
% Number of atoms : 222 ( 35 equ)
% Maximal formula atoms : 39 ( 3 avg)
% Number of connectives : 274 ( 113 ~; 115 |; 29 &)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 81 ( 0 sgn 41 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4730,hypothesis,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk)) )
=> sdtlpdtrp0(xd,X1) = sdtlpdtrp0(sdtlpdtrp0(xC,X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).
fof(mPttSet,axiom,
! [X1,X2] :
( ( aFunction0(X1)
& aElement0(X2) )
=> aSubsetOf0(sdtlbdtrb0(X1,X2),szDzozmdt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPttSet) ).
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__4758,hypothesis,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4758) ).
fof(mImgRng,axiom,
! [X1] :
( aFunction0(X1)
=> ! [X2] :
( aElementOf0(X2,szDzozmdt0(X1))
=> aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgRng) ).
fof(mDefPtt,axiom,
! [X1,X2] :
( ( aFunction0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtlbdtrb0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElementOf0(X4,szDzozmdt0(X1))
& sdtlpdtrp0(X1,X4) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPtt) ).
fof(m__3291,hypothesis,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(mDirichlet,axiom,
! [X1] :
( aFunction0(X1)
=> ( ( isCountable0(szDzozmdt0(X1))
& isFinite0(sdtlcdtrc0(X1,szDzozmdt0(X1))) )
=> ( aElement0(szDzizrdt0(X1))
& isCountable0(sdtlbdtrb0(X1,szDzizrdt0(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDirichlet) ).
fof(mSubFSet,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aSubsetOf0(X2,X1)
=> isFinite0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
fof(mCountNFin_01,axiom,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> X1 != slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(m__,conjecture,
aElementOf0(szDzizrdt0(xd),xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_13,hypothesis,
! [X365,X366] :
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ( ~ aElementOf0(X365,szNzAzT0)
| ~ aSet0(X366)
| ~ aElementOf0(X366,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X365)),xk))
| sdtlpdtrp0(xd,X365) = sdtlpdtrp0(sdtlpdtrp0(xC,X365),X366) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4730])])]) ).
fof(c_0_14,plain,
! [X311,X312] :
( ~ aFunction0(X311)
| ~ aElement0(X312)
| aSubsetOf0(sdtlbdtrb0(X311,X312),szDzozmdt0(X311)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPttSet])]) ).
fof(c_0_15,plain,
! [X184,X185,X186,X187] :
( ( aSet0(X185)
| ~ aSubsetOf0(X185,X184)
| ~ aSet0(X184) )
& ( ~ aElementOf0(X186,X185)
| aElementOf0(X186,X184)
| ~ aSubsetOf0(X185,X184)
| ~ aSet0(X184) )
& ( aElementOf0(esk2_2(X184,X187),X187)
| ~ aSet0(X187)
| aSubsetOf0(X187,X184)
| ~ aSet0(X184) )
& ( ~ aElementOf0(esk2_2(X184,X187),X184)
| ~ aSet0(X187)
| aSubsetOf0(X187,X184)
| ~ aSet0(X184) ) ),
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_16,hypothesis,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
inference(split_conjunct,[status(thm)],[m__4758]) ).
cnf(c_0_17,hypothesis,
szDzozmdt0(xd) = szNzAzT0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X324,X325] :
( ~ aFunction0(X324)
| ~ aElementOf0(X325,szDzozmdt0(X324))
| aElementOf0(sdtlpdtrp0(X324,X325),sdtlcdtrc0(X324,szDzozmdt0(X324))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgRng])])]) ).
fof(c_0_19,plain,
! [X304,X305,X306,X307,X308,X309] :
( ( aSet0(X306)
| X306 != sdtlbdtrb0(X304,X305)
| ~ aFunction0(X304)
| ~ aElement0(X305) )
& ( aElementOf0(X307,szDzozmdt0(X304))
| ~ aElementOf0(X307,X306)
| X306 != sdtlbdtrb0(X304,X305)
| ~ aFunction0(X304)
| ~ aElement0(X305) )
& ( sdtlpdtrp0(X304,X307) = X305
| ~ aElementOf0(X307,X306)
| X306 != sdtlbdtrb0(X304,X305)
| ~ aFunction0(X304)
| ~ aElement0(X305) )
& ( ~ aElementOf0(X308,szDzozmdt0(X304))
| sdtlpdtrp0(X304,X308) != X305
| aElementOf0(X308,X306)
| X306 != sdtlbdtrb0(X304,X305)
| ~ aFunction0(X304)
| ~ aElement0(X305) )
& ( ~ aElementOf0(esk13_3(X304,X305,X309),X309)
| ~ aElementOf0(esk13_3(X304,X305,X309),szDzozmdt0(X304))
| sdtlpdtrp0(X304,esk13_3(X304,X305,X309)) != X305
| ~ aSet0(X309)
| X309 = sdtlbdtrb0(X304,X305)
| ~ aFunction0(X304)
| ~ aElement0(X305) )
& ( aElementOf0(esk13_3(X304,X305,X309),szDzozmdt0(X304))
| aElementOf0(esk13_3(X304,X305,X309),X309)
| ~ aSet0(X309)
| X309 = sdtlbdtrb0(X304,X305)
| ~ aFunction0(X304)
| ~ aElement0(X305) )
& ( sdtlpdtrp0(X304,esk13_3(X304,X305,X309)) = X305
| aElementOf0(esk13_3(X304,X305,X309),X309)
| ~ aSet0(X309)
| X309 = sdtlbdtrb0(X304,X305)
| ~ aFunction0(X304)
| ~ aElement0(X305) ) ),
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)],[mDefPtt])])])])])]) ).
cnf(c_0_20,plain,
( aSubsetOf0(sdtlbdtrb0(X1,X2),szDzozmdt0(X1))
| ~ aFunction0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,hypothesis,
aFunction0(xd),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,hypothesis,
aSubsetOf0(sdtlcdtrc0(xd,szNzAzT0),xT),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,hypothesis,
aSet0(xT),
inference(split_conjunct,[status(thm)],[m__3291]) ).
cnf(c_0_25,plain,
( aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1)))
| ~ aFunction0(X1)
| ~ aElementOf0(X2,szDzozmdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( sdtlpdtrp0(X1,X2) = X3
| ~ aElementOf0(X2,X4)
| X4 != sdtlbdtrb0(X1,X3)
| ~ aFunction0(X1)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X178,X179,X180] :
( ( aSet0(X178)
| X178 != slcrc0 )
& ( ~ aElementOf0(X179,X178)
| X178 != slcrc0 )
& ( ~ aSet0(X180)
| aElementOf0(esk1_1(X180),X180)
| X180 = 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_28,plain,
( aSet0(X1)
| X1 != sdtlbdtrb0(X2,X3)
| ~ aFunction0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,hypothesis,
( aSubsetOf0(sdtlbdtrb0(xd,X1),szNzAzT0)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_17]),c_0_21])]) ).
cnf(c_0_30,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_31,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_32,plain,
! [X336] :
( ( aElement0(szDzizrdt0(X336))
| ~ isCountable0(szDzozmdt0(X336))
| ~ isFinite0(sdtlcdtrc0(X336,szDzozmdt0(X336)))
| ~ aFunction0(X336) )
& ( isCountable0(sdtlbdtrb0(X336,szDzizrdt0(X336)))
| ~ isCountable0(szDzozmdt0(X336))
| ~ isFinite0(sdtlcdtrc0(X336,szDzozmdt0(X336)))
| ~ aFunction0(X336) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDirichlet])])]) ).
fof(c_0_33,plain,
! [X189,X190] :
( ~ aSet0(X189)
| ~ isFinite0(X189)
| ~ aSubsetOf0(X190,X189)
| isFinite0(X190) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubFSet])])]) ).
cnf(c_0_34,hypothesis,
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,sdtlcdtrc0(xd,szNzAzT0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_35,hypothesis,
( aElementOf0(sdtlpdtrp0(xd,X1),sdtlcdtrc0(xd,szNzAzT0))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_17]),c_0_21])]) ).
cnf(c_0_36,plain,
( sdtlpdtrp0(X1,X2) = X3
| ~ aFunction0(X1)
| ~ aElementOf0(X2,sdtlbdtrb0(X1,X3))
| ~ aElement0(X3) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
( aElementOf0(esk1_1(X1),X1)
| X1 = slcrc0
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
( aSet0(sdtlbdtrb0(X1,X2))
| ~ aFunction0(X1)
| ~ aElement0(X2) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_39,hypothesis,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlbdtrb0(xd,X2))
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_29]),c_0_30])]) ).
cnf(c_0_40,hypothesis,
( aSet0(sdtlbdtrb0(xd,X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_29]),c_0_30])]) ).
cnf(c_0_41,plain,
( aElement0(szDzizrdt0(X1))
| ~ isCountable0(szDzozmdt0(X1))
| ~ isFinite0(sdtlcdtrc0(X1,szDzozmdt0(X1)))
| ~ aFunction0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
isCountable0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_43,plain,
( isFinite0(X2)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,hypothesis,
isFinite0(xT),
inference(split_conjunct,[status(thm)],[m__3291]) ).
fof(c_0_45,plain,
! [X183] :
( ~ aSet0(X183)
| ~ isCountable0(X183)
| X183 != slcrc0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCountNFin_01])]) ).
cnf(c_0_46,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_47,hypothesis,
( aElementOf0(sdtlpdtrp0(xd,X1),xT)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_48,plain,
( sdtlpdtrp0(X1,esk1_1(sdtlbdtrb0(X1,X2))) = X2
| sdtlbdtrb0(X1,X2) = slcrc0
| ~ aFunction0(X1)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_49,hypothesis,
( sdtlbdtrb0(xd,X1) = slcrc0
| aElementOf0(esk1_1(sdtlbdtrb0(xd,X1)),szNzAzT0)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_37]),c_0_40]) ).
cnf(c_0_50,hypothesis,
( aElement0(szDzizrdt0(xd))
| ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_17]),c_0_21]),c_0_42])]) ).
cnf(c_0_51,hypothesis,
isFinite0(sdtlcdtrc0(xd,szNzAzT0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_23]),c_0_44]),c_0_24])]) ).
cnf(c_0_52,plain,
( ~ aSet0(X1)
| ~ isCountable0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,plain,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_46]) ).
fof(c_0_54,negated_conjecture,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_55,plain,
( isCountable0(sdtlbdtrb0(X1,szDzizrdt0(X1)))
| ~ isCountable0(szDzozmdt0(X1))
| ~ isFinite0(sdtlcdtrc0(X1,szDzozmdt0(X1)))
| ~ aFunction0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_56,hypothesis,
( sdtlbdtrb0(xd,X1) = slcrc0
| aElementOf0(X1,xT)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_21])]),c_0_49]) ).
cnf(c_0_57,hypothesis,
aElement0(szDzizrdt0(xd)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).
cnf(c_0_58,plain,
~ isCountable0(slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_52]),c_0_53])]) ).
cnf(c_0_59,negated_conjecture,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_60,hypothesis,
$false,
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_21]),c_0_17]),c_0_42]),c_0_17]),c_0_51]),c_0_57])]),c_0_58]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM596+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 : n018.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 00:48:47 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 6.78/4.64 % Version : CSE_E---1.7
% 6.78/4.64 % Problem : theBenchmark.p
% 6.78/4.64 % SZS status Theorem for theBenchmark.p
% 6.78/4.64 % SZS output start CNFRefutation
% See solution above
% 6.78/4.66 % Total time : 3.374s
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