%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM563+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 : n021.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 04:57:50 PM UTC 2026
% Result : Theorem 6.26s 4.60s
% Output : CNFRefutation 6.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 14 unt; 0 def)
% Number of atoms : 267 ( 53 equ)
% Maximal formula atoms : 88 ( 5 avg)
% Number of connectives : 350 ( 128 ~; 130 |; 71 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 63 ( 2 sgn 35 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( xK = sz00
=> ? [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(mCardEmpty,axiom,
! [X1] :
( aSet0(X1)
=> ( sbrdtbr0(X1) = sz00
<=> X1 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
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(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(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(c_0_7,negated_conjecture,
~ ( xK = sz00
=> ? [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_8,plain,
! [X243] :
( ( sbrdtbr0(X243) != sz00
| X243 = slcrc0
| ~ aSet0(X243) )
& ( X243 != slcrc0
| sbrdtbr0(X243) = sz00
| ~ aSet0(X243) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardEmpty])])]) ).
fof(c_0_9,negated_conjecture,
! [X363,X364,X367] :
( xK = sz00
& ( aSet0(esk32_2(X363,X364))
| aElementOf0(esk31_2(X363,X364),X364)
| ~ aSet0(X364)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( ~ aElementOf0(X367,esk32_2(X363,X364))
| aElementOf0(X367,X364)
| aElementOf0(esk31_2(X363,X364),X364)
| ~ aSet0(X364)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( aSubsetOf0(esk32_2(X363,X364),X364)
| aElementOf0(esk31_2(X363,X364),X364)
| ~ aSet0(X364)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( sbrdtbr0(esk32_2(X363,X364)) = xK
| aElementOf0(esk31_2(X363,X364),X364)
| ~ aSet0(X364)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( aElementOf0(esk32_2(X363,X364),slbdtsldtrb0(X364,xK))
| aElementOf0(esk31_2(X363,X364),X364)
| ~ aSet0(X364)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( sdtlpdtrp0(xc,esk32_2(X363,X364)) != X363
| aElementOf0(esk31_2(X363,X364),X364)
| ~ aSet0(X364)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( aSet0(esk32_2(X363,X364))
| ~ aElementOf0(esk31_2(X363,X364),xS)
| ~ aSet0(X364)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( ~ aElementOf0(X367,esk32_2(X363,X364))
| aElementOf0(X367,X364)
| ~ aElementOf0(esk31_2(X363,X364),xS)
| ~ aSet0(X364)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( aSubsetOf0(esk32_2(X363,X364),X364)
| ~ aElementOf0(esk31_2(X363,X364),xS)
| ~ aSet0(X364)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( sbrdtbr0(esk32_2(X363,X364)) = xK
| ~ aElementOf0(esk31_2(X363,X364),xS)
| ~ aSet0(X364)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( aElementOf0(esk32_2(X363,X364),slbdtsldtrb0(X364,xK))
| ~ aElementOf0(esk31_2(X363,X364),xS)
| ~ aSet0(X364)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( sdtlpdtrp0(xc,esk32_2(X363,X364)) != X363
| ~ aElementOf0(esk31_2(X363,X364),xS)
| ~ aSet0(X364)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( aSet0(esk32_2(X363,X364))
| ~ aSubsetOf0(X364,xS)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( ~ aElementOf0(X367,esk32_2(X363,X364))
| aElementOf0(X367,X364)
| ~ aSubsetOf0(X364,xS)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( aSubsetOf0(esk32_2(X363,X364),X364)
| ~ aSubsetOf0(X364,xS)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( sbrdtbr0(esk32_2(X363,X364)) = xK
| ~ aSubsetOf0(X364,xS)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( aElementOf0(esk32_2(X363,X364),slbdtsldtrb0(X364,xK))
| ~ aSubsetOf0(X364,xS)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,xT) )
& ( sdtlpdtrp0(xc,esk32_2(X363,X364)) != X363
| ~ aSubsetOf0(X364,xS)
| ~ isCountable0(X364)
| ~ aElementOf0(X363,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_7])])])])]) ).
fof(c_0_10,plain,
! [X176,X177,X178] :
( ( aSet0(X176)
| X176 != slcrc0 )
& ( ~ aElementOf0(X177,X176)
| X176 != slcrc0 )
& ( ~ aSet0(X178)
| aElementOf0(esk1_1(X178),X178)
| X178 = 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_11,plain,
( sbrdtbr0(X1) = sz00
| X1 != slcrc0
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
xK = sz00,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,hypothesis,
! [X336,X337,X338,X340,X342,X343,X344] :
( aFunction0(xc)
& ( aSet0(X336)
| ~ aElementOf0(X336,szDzozmdt0(xc)) )
& ( ~ aElementOf0(X337,X336)
| aElementOf0(X337,xS)
| ~ aElementOf0(X336,szDzozmdt0(xc)) )
& ( aSubsetOf0(X336,xS)
| ~ aElementOf0(X336,szDzozmdt0(xc)) )
& ( sbrdtbr0(X336) = xK
| ~ aElementOf0(X336,szDzozmdt0(xc)) )
& ( aElementOf0(esk20_1(X338),X338)
| ~ aSet0(X338)
| sbrdtbr0(X338) != xK
| aElementOf0(X338,szDzozmdt0(xc)) )
& ( ~ aElementOf0(esk20_1(X338),xS)
| ~ aSet0(X338)
| sbrdtbr0(X338) != xK
| aElementOf0(X338,szDzozmdt0(xc)) )
& ( ~ aSubsetOf0(X338,xS)
| sbrdtbr0(X338) != xK
| aElementOf0(X338,szDzozmdt0(xc)) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ( aElementOf0(esk21_1(X340),szDzozmdt0(xc))
| ~ aElementOf0(X340,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ( sdtlpdtrp0(xc,esk21_1(X340)) = X340
| ~ aElementOf0(X340,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ( ~ aElementOf0(X343,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X343) != X342
| aElementOf0(X342,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& ( ~ aElementOf0(X344,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X344,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])])])])])]) ).
cnf(c_0_15,plain,
( sbrdtbr0(X1) = xK
| X1 != slcrc0 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_16,plain,
( ~ aElementOf0(X1,X2)
| X2 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,plain,
! [X322,X323] :
( ~ aFunction0(X322)
| ~ aElementOf0(X323,szDzozmdt0(X322))
| aElementOf0(sdtlpdtrp0(X322,X323),sdtlcdtrc0(X322,szDzozmdt0(X322))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgRng])])]) ).
cnf(c_0_18,hypothesis,
( aElementOf0(esk20_1(X1),X1)
| aElementOf0(X1,szDzozmdt0(xc))
| ~ aSet0(X1)
| sbrdtbr0(X1) != xK ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
sbrdtbr0(slcrc0) = xK,
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
~ aElementOf0(X1,slcrc0),
inference(er,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X189] :
( ~ aSet0(X189)
| aSubsetOf0(X189,X189) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])]) ).
fof(c_0_23,hypothesis,
! [X335] :
( aSet0(xS)
& ( ~ aElementOf0(X335,xS)
| aElementOf0(X335,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_24,plain,
( aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1)))
| ~ aFunction0(X1)
| ~ aElementOf0(X2,szDzozmdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,hypothesis,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_26,hypothesis,
aFunction0(xc),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,negated_conjecture,
( sbrdtbr0(esk32_2(X1,X2)) = xK
| ~ aSubsetOf0(X2,xS)
| ~ isCountable0(X2)
| ~ aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,plain,
( aSubsetOf0(X1,X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,hypothesis,
isCountable0(xS),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,hypothesis,
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_32,hypothesis,
aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_33,negated_conjecture,
( aSet0(esk32_2(X1,X2))
| ~ aSubsetOf0(X2,xS)
| ~ isCountable0(X2)
| ~ aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_34,plain,
( X1 = slcrc0
| sbrdtbr0(X1) != sz00
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_35,negated_conjecture,
( sbrdtbr0(esk32_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_27,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_36,hypothesis,
aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( aSet0(esk32_2(X1,xS))
| ~ aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_38,negated_conjecture,
( sdtlpdtrp0(xc,esk32_2(X1,X2)) != X1
| ~ aSubsetOf0(X2,xS)
| ~ isCountable0(X2)
| ~ aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_39,plain,
( X1 = slcrc0
| sbrdtbr0(X1) != xK
| ~ aSet0(X1) ),
inference(rw,[status(thm)],[c_0_34,c_0_12]) ).
cnf(c_0_40,negated_conjecture,
sbrdtbr0(esk32_2(sdtlpdtrp0(xc,slcrc0),xS)) = xK,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
aSet0(esk32_2(sdtlpdtrp0(xc,slcrc0),xS)),
inference(spm,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( sdtlpdtrp0(xc,esk32_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_38,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_43,negated_conjecture,
esk32_2(sdtlpdtrp0(xc,slcrc0),xS) = slcrc0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_44,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_36]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM563+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n021.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:46:25 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 6.26/4.60 % Version : CSE_E---1.7
% 6.26/4.60 % Problem : theBenchmark.p
% 6.26/4.60 % SZS status Theorem for theBenchmark.p
% 6.26/4.60 % SZS output start CNFRefutation
% See solution above
% 6.26/4.61 % Total time : 3.770s
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