%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM600+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.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 04:57:59 PM UTC 2026
% Result : Theorem 1.49s 1.80s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 11 unt; 0 def)
% Number of atoms : 203 ( 49 equ)
% Maximal formula atoms : 39 ( 4 avg)
% Number of connectives : 267 ( 107 ~; 110 |; 35 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-4 aty)
% Number of variables : 73 ( 0 sgn 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSImg,axiom,
! [X1] :
( aFunction0(X1)
=> ! [X2] :
( aSubsetOf0(X2,szDzozmdt0(X1))
=> ! [X3] :
( X3 = sdtlcdtrc0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ? [X5] :
( aElementOf0(X5,X2)
& sdtlpdtrp0(X1,X5) = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSImg) ).
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/sandbox/benchmark/theBenchmark.p',mDefPtt) ).
fof(m__4660,hypothesis,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__,conjecture,
! [X1] :
( aElementOf0(X1,xO)
=> ? [X2] :
( aElementOf0(X2,szNzAzT0)
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__4891,hypothesis,
( aSet0(xO)
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
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/sandbox/benchmark/theBenchmark.p',m__4730) ).
fof(m__4854,hypothesis,
( aElementOf0(szDzizrdt0(xd),xT)
& isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4854) ).
fof(m__3291,hypothesis,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
fof(mPttSet,axiom,
! [X1,X2] :
( ( aFunction0(X1)
& aElement0(X2) )
=> aSubsetOf0(sdtlbdtrb0(X1,X2),szDzozmdt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPttSet) ).
fof(c_0_10,plain,
! [X315,X316,X317,X318,X320,X321,X322,X324] :
( ( aSet0(X317)
| X317 != sdtlcdtrc0(X315,X316)
| ~ aSubsetOf0(X316,szDzozmdt0(X315))
| ~ aFunction0(X315) )
& ( aElementOf0(esk14_4(X315,X316,X317,X318),X316)
| ~ aElementOf0(X318,X317)
| X317 != sdtlcdtrc0(X315,X316)
| ~ aSubsetOf0(X316,szDzozmdt0(X315))
| ~ aFunction0(X315) )
& ( sdtlpdtrp0(X315,esk14_4(X315,X316,X317,X318)) = X318
| ~ aElementOf0(X318,X317)
| X317 != sdtlcdtrc0(X315,X316)
| ~ aSubsetOf0(X316,szDzozmdt0(X315))
| ~ aFunction0(X315) )
& ( ~ aElementOf0(X321,X316)
| sdtlpdtrp0(X315,X321) != X320
| aElementOf0(X320,X317)
| X317 != sdtlcdtrc0(X315,X316)
| ~ aSubsetOf0(X316,szDzozmdt0(X315))
| ~ aFunction0(X315) )
& ( ~ aElementOf0(esk15_3(X315,X316,X322),X322)
| ~ aElementOf0(X324,X316)
| sdtlpdtrp0(X315,X324) != esk15_3(X315,X316,X322)
| ~ aSet0(X322)
| X322 = sdtlcdtrc0(X315,X316)
| ~ aSubsetOf0(X316,szDzozmdt0(X315))
| ~ aFunction0(X315) )
& ( aElementOf0(esk16_3(X315,X316,X322),X316)
| aElementOf0(esk15_3(X315,X316,X322),X322)
| ~ aSet0(X322)
| X322 = sdtlcdtrc0(X315,X316)
| ~ aSubsetOf0(X316,szDzozmdt0(X315))
| ~ aFunction0(X315) )
& ( sdtlpdtrp0(X315,esk16_3(X315,X316,X322)) = esk15_3(X315,X316,X322)
| aElementOf0(esk15_3(X315,X316,X322),X322)
| ~ aSet0(X322)
| X322 = sdtlcdtrc0(X315,X316)
| ~ aSubsetOf0(X316,szDzozmdt0(X315))
| ~ aFunction0(X315) ) ),
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)],[mDefSImg])])])])])]) ).
fof(c_0_11,plain,
! [X306,X307,X308,X309,X310,X311] :
( ( aSet0(X308)
| X308 != sdtlbdtrb0(X306,X307)
| ~ aFunction0(X306)
| ~ aElement0(X307) )
& ( aElementOf0(X309,szDzozmdt0(X306))
| ~ aElementOf0(X309,X308)
| X308 != sdtlbdtrb0(X306,X307)
| ~ aFunction0(X306)
| ~ aElement0(X307) )
& ( sdtlpdtrp0(X306,X309) = X307
| ~ aElementOf0(X309,X308)
| X308 != sdtlbdtrb0(X306,X307)
| ~ aFunction0(X306)
| ~ aElement0(X307) )
& ( ~ aElementOf0(X310,szDzozmdt0(X306))
| sdtlpdtrp0(X306,X310) != X307
| aElementOf0(X310,X308)
| X308 != sdtlbdtrb0(X306,X307)
| ~ aFunction0(X306)
| ~ aElement0(X307) )
& ( ~ aElementOf0(esk13_3(X306,X307,X311),X311)
| ~ aElementOf0(esk13_3(X306,X307,X311),szDzozmdt0(X306))
| sdtlpdtrp0(X306,esk13_3(X306,X307,X311)) != X307
| ~ aSet0(X311)
| X311 = sdtlbdtrb0(X306,X307)
| ~ aFunction0(X306)
| ~ aElement0(X307) )
& ( aElementOf0(esk13_3(X306,X307,X311),szDzozmdt0(X306))
| aElementOf0(esk13_3(X306,X307,X311),X311)
| ~ aSet0(X311)
| X311 = sdtlbdtrb0(X306,X307)
| ~ aFunction0(X306)
| ~ aElement0(X307) )
& ( sdtlpdtrp0(X306,esk13_3(X306,X307,X311)) = X307
| aElementOf0(esk13_3(X306,X307,X311),X311)
| ~ aSet0(X311)
| X311 = sdtlbdtrb0(X306,X307)
| ~ aFunction0(X306)
| ~ aElement0(X307) ) ),
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_12,plain,
( aElementOf0(esk14_4(X1,X2,X3,X4),X2)
| ~ aElementOf0(X4,X3)
| X3 != sdtlcdtrc0(X1,X2)
| ~ aSubsetOf0(X2,szDzozmdt0(X1))
| ~ aFunction0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,hypothesis,
! [X366] :
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ( ~ aElementOf0(X366,szNzAzT0)
| sdtlpdtrp0(xe,X366) = szmzizndt0(sdtlpdtrp0(xN,X366)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4660])])]) ).
fof(c_0_14,plain,
! [X178,X179] :
( ~ aSet0(X178)
| ~ aElementOf0(X179,X178)
| aElement0(X179) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( aElementOf0(X1,xO)
=> ? [X2] :
( aElementOf0(X2,szNzAzT0)
& aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X2) = X1 ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_16,plain,
( aElementOf0(X1,szDzozmdt0(X2))
| ~ aElementOf0(X1,X3)
| X3 != sdtlbdtrb0(X2,X4)
| ~ aFunction0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( aElementOf0(esk14_4(X1,X2,sdtlcdtrc0(X1,X2),X3),X2)
| ~ aFunction0(X1)
| ~ aSubsetOf0(X2,szDzozmdt0(X1))
| ~ aElementOf0(X3,sdtlcdtrc0(X1,X2)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_18,hypothesis,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(split_conjunct,[status(thm)],[m__4891]) ).
cnf(c_0_19,hypothesis,
aFunction0(xe),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,hypothesis,
szDzozmdt0(xe) = szNzAzT0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_21,hypothesis,
! [X367,X368] :
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ( ~ aElementOf0(X367,szNzAzT0)
| ~ aSet0(X368)
| ~ aElementOf0(X368,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X367)),xk))
| sdtlpdtrp0(xd,X367) = sdtlpdtrp0(sdtlpdtrp0(xC,X367),X368) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4730])])]) ).
cnf(c_0_22,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
aElementOf0(szDzizrdt0(xd),xT),
inference(split_conjunct,[status(thm)],[m__4854]) ).
cnf(c_0_24,hypothesis,
aSet0(xT),
inference(split_conjunct,[status(thm)],[m__3291]) ).
fof(c_0_25,negated_conjecture,
! [X370] :
( aElementOf0(esk25_0,xO)
& ( ~ aElementOf0(X370,szNzAzT0)
| ~ aElementOf0(X370,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X370) != esk25_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_26,plain,
( aElementOf0(X1,szDzozmdt0(X2))
| ~ aFunction0(X2)
| ~ aElementOf0(X1,sdtlbdtrb0(X2,X3))
| ~ aElement0(X3) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_27,hypothesis,
( aElementOf0(esk14_4(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),xO,X1),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(X1,xO) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_28,hypothesis,
szDzozmdt0(xd) = szNzAzT0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
aFunction0(xd),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,hypothesis,
aElement0(szDzizrdt0(xd)),
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,
( sdtlpdtrp0(X1,esk14_4(X1,X2,X3,X4)) = X4
| ~ aElementOf0(X4,X3)
| X3 != sdtlcdtrc0(X1,X2)
| ~ aSubsetOf0(X2,szDzozmdt0(X1))
| ~ aFunction0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_32,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X1) != esk25_0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,hypothesis,
( aElementOf0(esk14_4(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),xO,X1),szNzAzT0)
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(X1,xO) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_34,plain,
( sdtlpdtrp0(X1,esk14_4(X1,X2,sdtlcdtrc0(X1,X2),X3)) = X3
| ~ aFunction0(X1)
| ~ aSubsetOf0(X2,szDzozmdt0(X1))
| ~ aElementOf0(X3,sdtlcdtrc0(X1,X2)) ),
inference(er,[status(thm)],[c_0_31]) ).
fof(c_0_35,plain,
! [X313,X314] :
( ~ aFunction0(X313)
| ~ aElement0(X314)
| aSubsetOf0(sdtlbdtrb0(X313,X314),szDzozmdt0(X313)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPttSet])]) ).
cnf(c_0_36,negated_conjecture,
( sdtlpdtrp0(xe,esk14_4(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),xO,X1)) != esk25_0
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(X1,xO) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_33]) ).
cnf(c_0_37,hypothesis,
( sdtlpdtrp0(xe,esk14_4(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),xO,X1)) = X1
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(X1,xO) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_38,negated_conjecture,
aElementOf0(esk25_0,xO),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_39,plain,
( aSubsetOf0(sdtlbdtrb0(X1,X2),szDzozmdt0(X1))
| ~ aFunction0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,negated_conjecture,
~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37])]),c_0_38])]) ).
cnf(c_0_41,hypothesis,
( aSubsetOf0(sdtlbdtrb0(xd,X1),szNzAzT0)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_28]),c_0_29])]) ).
cnf(c_0_42,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM600+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n005.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 00:50:00 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.49/1.80 % Version : CSE_E---1.7
% 1.49/1.80 % Problem : theBenchmark.p
% 1.49/1.80 % SZS status Theorem for theBenchmark.p
% 1.49/1.80 % SZS output start CNFRefutation
% See solution above
% 1.58/1.80 % Total time : 1.373s
%------------------------------------------------------------------------------