%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM566+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 : n001.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 1.34s 1.74s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 16 unt; 0 def)
% Number of atoms : 118 ( 13 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 126 ( 53 ~; 48 |; 16 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 19 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( aElementOf0(X1,xT)
& ? [X2] :
( aSubsetOf0(X2,xS)
& isCountable0(X2)
& ! [X3] :
( aElementOf0(X3,slbdtsldtrb0(X2,xK))
=> sdtlpdtrp0(xc,X3) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__3507,hypothesis,
! [X1] :
( aElementOf0(X1,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3507) ).
fof(m__3453,hypothesis,
( aFunction0(xc)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
fof(m__3462,hypothesis,
xK = sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(m__3435,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(m__3291,hypothesis,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
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__3476,hypothesis,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3476) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(c_0_11,negated_conjecture,
~ ? [X1] :
( aElementOf0(X1,xT)
& ? [X2] :
( aSubsetOf0(X2,xS)
& isCountable0(X2)
& ! [X3] :
( aElementOf0(X3,slbdtsldtrb0(X2,xK))
=> sdtlpdtrp0(xc,X3) = X1 ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,hypothesis,
! [X323] :
( ~ aElementOf0(X323,slbdtsldtrb0(xS,sz00))
| sdtlpdtrp0(xc,X323) = sdtlpdtrp0(xc,slcrc0) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3507])]) ).
cnf(c_0_13,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_14,hypothesis,
xK = sz00,
inference(split_conjunct,[status(thm)],[m__3462]) ).
fof(c_0_15,negated_conjecture,
! [X324,X325] :
( ( aElementOf0(esk22_2(X324,X325),slbdtsldtrb0(X325,xK))
| ~ aSubsetOf0(X325,xS)
| ~ isCountable0(X325)
| ~ aElementOf0(X324,xT) )
& ( sdtlpdtrp0(xc,esk22_2(X324,X325)) != X324
| ~ aSubsetOf0(X325,xS)
| ~ isCountable0(X325)
| ~ aElementOf0(X324,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_11])])])])]) ).
cnf(c_0_16,hypothesis,
( sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0)
| ~ aElementOf0(X1,slbdtsldtrb0(xS,sz00)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( aElementOf0(esk22_2(X1,X2),slbdtsldtrb0(X2,xK))
| ~ aSubsetOf0(X2,xS)
| ~ isCountable0(X2)
| ~ aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X164,X165,X166,X167] :
( ( aSet0(X165)
| ~ aSubsetOf0(X165,X164)
| ~ aSet0(X164) )
& ( ~ aElementOf0(X166,X165)
| aElementOf0(X166,X164)
| ~ aSubsetOf0(X165,X164)
| ~ aSet0(X164) )
& ( aElementOf0(esk2_2(X164,X167),X167)
| ~ aSet0(X167)
| aSubsetOf0(X167,X164)
| ~ aSet0(X164) )
& ( ~ aElementOf0(esk2_2(X164,X167),X164)
| ~ aSet0(X167)
| aSubsetOf0(X167,X164)
| ~ aSet0(X164) ) ),
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_20,negated_conjecture,
( sdtlpdtrp0(xc,esk22_2(X1,X2)) != X1
| ~ aSubsetOf0(X2,xS)
| ~ isCountable0(X2)
| ~ aElementOf0(X1,xT) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,hypothesis,
( sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0)
| ~ aElementOf0(X1,szDzozmdt0(xc)) ),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( aElementOf0(esk22_2(X1,X2),slbdtsldtrb0(X2,sz00))
| ~ aSubsetOf0(X2,xS)
| ~ isCountable0(X2)
| ~ aElementOf0(X1,xT) ),
inference(rw,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_23,hypothesis,
isCountable0(xS),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_24,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,hypothesis,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_26,hypothesis,
aSet0(xT),
inference(split_conjunct,[status(thm)],[m__3291]) ).
fof(c_0_27,plain,
! [X304,X305] :
( ~ aFunction0(X304)
| ~ aElementOf0(X305,szDzozmdt0(X304))
| aElementOf0(sdtlpdtrp0(X304,X305),sdtlcdtrc0(X304,szDzozmdt0(X304))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgRng])])]) ).
cnf(c_0_28,hypothesis,
( ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ~ aElementOf0(esk22_2(sdtlpdtrp0(xc,slcrc0),X1),szDzozmdt0(xc))
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]) ).
cnf(c_0_29,hypothesis,
( aElementOf0(esk22_2(X1,xS),szDzozmdt0(xc))
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_17]),c_0_23])]) ).
cnf(c_0_30,hypothesis,
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,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_31,plain,
( aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1)))
| ~ aFunction0(X1)
| ~ aElementOf0(X2,szDzozmdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,hypothesis,
aFunction0(xc),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_33,hypothesis,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(split_conjunct,[status(thm)],[m__3476]) ).
cnf(c_0_34,hypothesis,
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_23])]) ).
cnf(c_0_35,hypothesis,
( aElementOf0(sdtlpdtrp0(xc,X1),xT)
| ~ aElementOf0(X1,szDzozmdt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_36,hypothesis,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(rw,[status(thm)],[c_0_33,c_0_17]) ).
fof(c_0_37,plain,
! [X171] :
( ~ aSet0(X171)
| aSubsetOf0(X171,X171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])]) ).
cnf(c_0_38,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_39,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_40,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_41,hypothesis,
~ aSubsetOf0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_42,plain,
( aSubsetOf0(X1,X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_44,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM566+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
% 0.15/0.33 % Computer : n001.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 00:46:18 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.34/1.74 % Version : CSE_E---1.7
% 1.34/1.74 % Problem : theBenchmark.p
% 1.34/1.74 % SZS status Theorem for theBenchmark.p
% 1.34/1.74 % SZS output start CNFRefutation
% See solution above
% 1.34/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------