%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM574+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 : n024.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 04:57:52 PM UTC 2026
% Result : Theorem 1.16s 1.63s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 13 unt; 0 def)
% Number of atoms : 137 ( 26 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 147 ( 55 ~; 55 |; 23 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3786_02,hypothesis,
( ( sdtlseqdt0(xj,xi)
& ? [X1] :
( aElementOf0(X1,szNzAzT0)
& szszuzczcdt0(X1) = xi ) )
=> ( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786_02) ).
fof(m__,conjecture,
( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mNatExtra,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( X1 = sz00
| ? [X2] :
( aElementOf0(X2,szNzAzT0)
& X1 = szszuzczcdt0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(mLessASymm,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(m__3786,hypothesis,
( aElementOf0(xj,szNzAzT0)
& aElementOf0(xi,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786) ).
fof(m__3623,hypothesis,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(mZeroLess,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(sz00,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
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(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(m__3435,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(c_0_11,hypothesis,
! [X328] :
( ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X328,szNzAzT0)
| szszuzczcdt0(X328) != xi
| ~ sdtlseqdt0(xj,xi)
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3786_02])])]) ).
fof(c_0_12,negated_conjecture,
~ ( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_13,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(X1,szNzAzT0)
| szszuzczcdt0(X1) != xi
| ~ sdtlseqdt0(xj,xi) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,negated_conjecture,
( sdtlseqdt0(xj,xi)
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
cnf(c_0_15,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| szszuzczcdt0(X1) != xi
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(xj,xi) ),
inference(cn,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
sdtlseqdt0(xj,xi),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X207] :
( ( aElementOf0(esk5_1(X207),szNzAzT0)
| X207 = sz00
| ~ aElementOf0(X207,szNzAzT0) )
& ( X207 = szszuzczcdt0(esk5_1(X207))
| X207 = sz00
| ~ aElementOf0(X207,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNatExtra])])])]) ).
fof(c_0_19,plain,
! [X216,X217] :
( ~ aElementOf0(X216,szNzAzT0)
| ~ aElementOf0(X217,szNzAzT0)
| ~ sdtlseqdt0(X216,X217)
| ~ sdtlseqdt0(X217,X216)
| X216 = X217 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])]) ).
cnf(c_0_20,hypothesis,
( szszuzczcdt0(X1) != xi
| ~ aElementOf0(X1,szNzAzT0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),c_0_17]) ).
cnf(c_0_21,plain,
( X1 = szszuzczcdt0(esk5_1(X1))
| X1 = sz00
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3786]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
aElementOf0(xj,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3786]) ).
cnf(c_0_25,hypothesis,
( xi = sz00
| ~ aElementOf0(esk5_1(xi),szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]),c_0_22])]) ).
cnf(c_0_26,plain,
( aElementOf0(esk5_1(X1),szNzAzT0)
| X1 = sz00
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,hypothesis,
! [X324] :
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X324)),sdtmndt0(sdtlpdtrp0(xN,X324),szmzizndt0(sdtlpdtrp0(xN,X324))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X324),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X324))
| ~ aElementOf0(X324,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X324)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X324),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X324))
| ~ aElementOf0(X324,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3623])])])]) ).
cnf(c_0_28,negated_conjecture,
( xj = xi
| ~ sdtlseqdt0(xi,xj) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_16]),c_0_24]),c_0_22])]) ).
cnf(c_0_29,hypothesis,
xi = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_22])]) ).
fof(c_0_30,plain,
! [X210] :
( ~ aElementOf0(X210,szNzAzT0)
| sdtlseqdt0(sz00,X210) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])]) ).
cnf(c_0_31,hypothesis,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( xj = sz00
| ~ sdtlseqdt0(sz00,xj) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]) ).
cnf(c_0_33,plain,
( sdtlseqdt0(sz00,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_34,plain,
! [X165,X166,X167,X168] :
( ( aSet0(X166)
| ~ aSubsetOf0(X166,X165)
| ~ aSet0(X165) )
& ( ~ aElementOf0(X167,X166)
| aElementOf0(X167,X165)
| ~ aSubsetOf0(X166,X165)
| ~ aSet0(X165) )
& ( aElementOf0(esk2_2(X165,X168),X168)
| ~ aSet0(X168)
| aSubsetOf0(X168,X165)
| ~ aSet0(X165) )
& ( ~ aElementOf0(esk2_2(X165,X168),X165)
| ~ aSet0(X168)
| aSubsetOf0(X168,X165)
| ~ aSet0(X165) ) ),
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_35,negated_conjecture,
~ aSubsetOf0(xS,sdtlpdtrp0(xN,xj)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_29]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
xj = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_24])]) ).
fof(c_0_37,plain,
! [X172] :
( ~ aSet0(X172)
| aSubsetOf0(X172,X172) ),
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_34]) ).
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,negated_conjecture,
~ aSubsetOf0(xS,xS),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_31]) ).
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,negated_conjecture,
$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
% 0.00/0.06 % Problem : NUM574+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 19:46:41 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.16/1.63 % Version : CSE_E---1.7
% 1.16/1.63 % Problem : theBenchmark.p
% 1.16/1.63 % SZS status Theorem for theBenchmark.p
% 1.16/1.63 % SZS output start CNFRefutation
% See solution above
% 1.16/1.63 % Total time : 1.362s
%------------------------------------------------------------------------------