%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM566+3 : 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 : n014.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 04:57:51 PM UTC 2026
% Result : Theorem 6.21s 4.62s
% Output : CNFRefutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 14 unt; 0 def)
% Number of atoms : 253 ( 40 equ)
% Maximal formula atoms : 87 ( 6 avg)
% Number of connectives : 330 ( 117 ~; 119 |; 75 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 34 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3476,hypothesis,
( aSet0(slcrc0)
& ~ ? [X1] : aElementOf0(X1,slcrc0)
& ! [X1] :
( aElementOf0(X1,slcrc0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(slcrc0,xS)
& aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3476) ).
fof(m__3453,hypothesis,
( aFunction0(xc)
& ! [X1] :
( ( aElementOf0(X1,szDzozmdt0(xc))
=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSubsetOf0(X1,xS)
& sbrdtbr0(X1) = xK ) )
& ( ( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X1,xS) )
& sbrdtbr0(X1) = xK )
=> aElementOf0(X1,szDzozmdt0(xc)) ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X1] :
( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X2] :
( aElementOf0(X2,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(X1,xT) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
fof(m__,conjecture,
? [X1] :
( aElementOf0(X1,xT)
& ? [X2] :
( ( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,xS) ) )
| aSubsetOf0(X2,xS) )
& isCountable0(X2)
& ! [X3] :
( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,X2) )
& aSubsetOf0(X3,X2)
& sbrdtbr0(X3) = xK
& aElementOf0(X3,slbdtsldtrb0(X2,xK)) )
=> sdtlpdtrp0(xc,X3) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mImgRng,axiom,
! [X1] :
( aFunction0(X1)
=> ! [X2] :
( aElementOf0(X2,szDzozmdt0(X1))
=> aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgRng) ).
fof(m__3462,hypothesis,
xK = sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(m__3435,hypothesis,
( aSet0(xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(mCardEmpty,axiom,
! [X1] :
( aSet0(X1)
=> ( sbrdtbr0(X1) = sz00
<=> X1 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
fof(c_0_8,hypothesis,
! [X368,X369] :
( aSet0(slcrc0)
& ~ aElementOf0(X368,slcrc0)
& ( ~ aElementOf0(X369,slcrc0)
| aElementOf0(X369,xS) )
& aSubsetOf0(slcrc0,xS)
& aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3476])])]) ).
fof(c_0_9,hypothesis,
! [X341,X342,X343,X345,X347,X348,X349] :
( aFunction0(xc)
& ( aSet0(X341)
| ~ aElementOf0(X341,szDzozmdt0(xc)) )
& ( ~ aElementOf0(X342,X341)
| aElementOf0(X342,xS)
| ~ aElementOf0(X341,szDzozmdt0(xc)) )
& ( aSubsetOf0(X341,xS)
| ~ aElementOf0(X341,szDzozmdt0(xc)) )
& ( sbrdtbr0(X341) = xK
| ~ aElementOf0(X341,szDzozmdt0(xc)) )
& ( aElementOf0(esk20_1(X343),X343)
| ~ aSet0(X343)
| sbrdtbr0(X343) != xK
| aElementOf0(X343,szDzozmdt0(xc)) )
& ( ~ aElementOf0(esk20_1(X343),xS)
| ~ aSet0(X343)
| sbrdtbr0(X343) != xK
| aElementOf0(X343,szDzozmdt0(xc)) )
& ( ~ aSubsetOf0(X343,xS)
| sbrdtbr0(X343) != xK
| aElementOf0(X343,szDzozmdt0(xc)) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ( aElementOf0(esk21_1(X345),szDzozmdt0(xc))
| ~ aElementOf0(X345,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ( sdtlpdtrp0(xc,esk21_1(X345)) = X345
| ~ aElementOf0(X345,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ( ~ aElementOf0(X348,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X348) != X347
| aElementOf0(X347,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ( ~ aElementOf0(X349,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X349,xT) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
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)],[m__3453])])])])])]) ).
fof(c_0_10,negated_conjecture,
~ ? [X1] :
( aElementOf0(X1,xT)
& ? [X2] :
( ( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,xS) ) )
| aSubsetOf0(X2,xS) )
& isCountable0(X2)
& ! [X3] :
( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,X2) )
& aSubsetOf0(X3,X2)
& sbrdtbr0(X3) = xK
& aElementOf0(X3,slbdtsldtrb0(X2,xK)) )
=> sdtlpdtrp0(xc,X3) = X1 ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_11,plain,
! [X327,X328] :
( ~ aFunction0(X327)
| ~ aElementOf0(X328,szDzozmdt0(X327))
| aElementOf0(sdtlpdtrp0(X327,X328),sdtlcdtrc0(X327,szDzozmdt0(X327))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgRng])])]) ).
cnf(c_0_12,hypothesis,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
xK = sz00,
inference(split_conjunct,[status(thm)],[m__3462]) ).
cnf(c_0_14,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,negated_conjecture,
! [X373,X374,X377] :
( ( aSet0(esk33_2(X373,X374))
| aElementOf0(esk32_2(X373,X374),X374)
| ~ aSet0(X374)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( ~ aElementOf0(X377,esk33_2(X373,X374))
| aElementOf0(X377,X374)
| aElementOf0(esk32_2(X373,X374),X374)
| ~ aSet0(X374)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( aSubsetOf0(esk33_2(X373,X374),X374)
| aElementOf0(esk32_2(X373,X374),X374)
| ~ aSet0(X374)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( sbrdtbr0(esk33_2(X373,X374)) = xK
| aElementOf0(esk32_2(X373,X374),X374)
| ~ aSet0(X374)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( aElementOf0(esk33_2(X373,X374),slbdtsldtrb0(X374,xK))
| aElementOf0(esk32_2(X373,X374),X374)
| ~ aSet0(X374)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( sdtlpdtrp0(xc,esk33_2(X373,X374)) != X373
| aElementOf0(esk32_2(X373,X374),X374)
| ~ aSet0(X374)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( aSet0(esk33_2(X373,X374))
| ~ aElementOf0(esk32_2(X373,X374),xS)
| ~ aSet0(X374)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( ~ aElementOf0(X377,esk33_2(X373,X374))
| aElementOf0(X377,X374)
| ~ aElementOf0(esk32_2(X373,X374),xS)
| ~ aSet0(X374)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( aSubsetOf0(esk33_2(X373,X374),X374)
| ~ aElementOf0(esk32_2(X373,X374),xS)
| ~ aSet0(X374)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( sbrdtbr0(esk33_2(X373,X374)) = xK
| ~ aElementOf0(esk32_2(X373,X374),xS)
| ~ aSet0(X374)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( aElementOf0(esk33_2(X373,X374),slbdtsldtrb0(X374,xK))
| ~ aElementOf0(esk32_2(X373,X374),xS)
| ~ aSet0(X374)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( sdtlpdtrp0(xc,esk33_2(X373,X374)) != X373
| ~ aElementOf0(esk32_2(X373,X374),xS)
| ~ aSet0(X374)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( aSet0(esk33_2(X373,X374))
| ~ aSubsetOf0(X374,xS)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( ~ aElementOf0(X377,esk33_2(X373,X374))
| aElementOf0(X377,X374)
| ~ aSubsetOf0(X374,xS)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( aSubsetOf0(esk33_2(X373,X374),X374)
| ~ aSubsetOf0(X374,xS)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( sbrdtbr0(esk33_2(X373,X374)) = xK
| ~ aSubsetOf0(X374,xS)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( aElementOf0(esk33_2(X373,X374),slbdtsldtrb0(X374,xK))
| ~ aSubsetOf0(X374,xS)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) )
& ( sdtlpdtrp0(xc,esk33_2(X373,X374)) != X373
| ~ aSubsetOf0(X374,xS)
| ~ isCountable0(X374)
| ~ aElementOf0(X373,xT) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
fof(c_0_16,plain,
! [X194] :
( ~ aSet0(X194)
| aSubsetOf0(X194,X194) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])]) ).
fof(c_0_17,hypothesis,
! [X340] :
( aSet0(xS)
& ( ~ aElementOf0(X340,xS)
| aElementOf0(X340,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3435])])]) ).
cnf(c_0_18,plain,
( aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1)))
| ~ aFunction0(X1)
| ~ aElementOf0(X2,szDzozmdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,hypothesis,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_20,hypothesis,
aFunction0(xc),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_21,plain,
! [X248] :
( ( sbrdtbr0(X248) != sz00
| X248 = slcrc0
| ~ aSet0(X248) )
& ( X248 != slcrc0
| sbrdtbr0(X248) = sz00
| ~ aSet0(X248) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardEmpty])])]) ).
cnf(c_0_22,negated_conjecture,
( sbrdtbr0(esk33_2(X1,X2)) = xK
| ~ aSubsetOf0(X2,xS)
| ~ isCountable0(X2)
| ~ aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( aSubsetOf0(X1,X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,hypothesis,
isCountable0(xS),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,hypothesis,
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,hypothesis,
aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_28,negated_conjecture,
( aSet0(esk33_2(X1,X2))
| ~ aSubsetOf0(X2,xS)
| ~ isCountable0(X2)
| ~ aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,plain,
( X1 = slcrc0
| sbrdtbr0(X1) != sz00
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
( sbrdtbr0(esk33_2(X1,xS)) = xK
| ~ aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_31,hypothesis,
aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( aSet0(esk33_2(X1,xS))
| ~ aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_33,negated_conjecture,
( sdtlpdtrp0(xc,esk33_2(X1,X2)) != X1
| ~ aSubsetOf0(X2,xS)
| ~ isCountable0(X2)
| ~ aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_34,plain,
( X1 = slcrc0
| sbrdtbr0(X1) != xK
| ~ aSet0(X1) ),
inference(rw,[status(thm)],[c_0_29,c_0_13]) ).
cnf(c_0_35,negated_conjecture,
sbrdtbr0(esk33_2(sdtlpdtrp0(xc,slcrc0),xS)) = xK,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
aSet0(esk33_2(sdtlpdtrp0(xc,slcrc0),xS)),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( sdtlpdtrp0(xc,esk33_2(X1,xS)) != X1
| ~ aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_38,negated_conjecture,
esk33_2(sdtlpdtrp0(xc,slcrc0),xS) = slcrc0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_31]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM566+3 : 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
% 0.16/0.33 % Computer : n014.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:46:36 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 6.21/4.62 % Version : CSE_E---1.7
% 6.21/4.62 % Problem : theBenchmark.p
% 6.21/4.62 % SZS status Theorem for theBenchmark.p
% 6.21/4.62 % SZS output start CNFRefutation
% See solution above
% 6.21/4.63 % Total time : 3.766s
%------------------------------------------------------------------------------