%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM597+3 : 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 : n025.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 04:57:58 PM UTC 2026
% Result : Theorem 4.19s 3.51s
% Output : CNFRefutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 11 unt; 0 def)
% Number of atoms : 95 ( 20 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 107 ( 38 ~; 36 |; 24 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 17 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4868,hypothesis,
~ ( ( aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X1] :
( aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(X1,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X1) = szDzizrdt0(xd) ) ) )
=> ~ ? [X1] : aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4868) ).
fof(m__4730,hypothesis,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aSet0(X2)
& ( ( ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtlpdtrp0(xN,szszuzczcdt0(X1))) )
| aSubsetOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X1))) )
& sbrdtbr0(X2) = xk )
| aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk)) ) )
=> sdtlpdtrp0(xd,X1) = sdtlpdtrp0(sdtlpdtrp0(xC,X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).
fof(mImgRng,axiom,
! [X1] :
( aFunction0(X1)
=> ! [X2] :
( aElementOf0(X2,szDzozmdt0(X1))
=> aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgRng) ).
fof(m__4758,hypothesis,
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ! [X1] :
( aElementOf0(X1,sdtlcdtrc0(xd,szDzozmdt0(xd)))
<=> ? [X2] :
( aElementOf0(X2,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,sdtlcdtrc0(xd,szDzozmdt0(xd)))
=> aElementOf0(X1,xT) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4758) ).
fof(m__,conjecture,
aElementOf0(szDzizrdt0(xd),xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_5,hypothesis,
! [X467] :
( aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ( aElementOf0(X467,szDzozmdt0(xd))
| ~ aElementOf0(X467,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ( sdtlpdtrp0(xd,X467) = szDzizrdt0(xd)
| ~ aElementOf0(X467,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& ( ~ aElementOf0(X467,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X467) != szDzizrdt0(xd)
| aElementOf0(X467,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& aElementOf0(esk38_0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4868])])])])]) ).
fof(c_0_6,hypothesis,
! [X459,X460] :
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ( aElementOf0(esk36_2(X459,X460),X460)
| sbrdtbr0(X460) != xk
| ~ aSet0(X460)
| sdtlpdtrp0(xd,X459) = sdtlpdtrp0(sdtlpdtrp0(xC,X459),X460)
| ~ aElementOf0(X459,szNzAzT0) )
& ( ~ aElementOf0(esk36_2(X459,X460),sdtlpdtrp0(xN,szszuzczcdt0(X459)))
| sbrdtbr0(X460) != xk
| ~ aSet0(X460)
| sdtlpdtrp0(xd,X459) = sdtlpdtrp0(sdtlpdtrp0(xC,X459),X460)
| ~ aElementOf0(X459,szNzAzT0) )
& ( ~ aSubsetOf0(X460,sdtlpdtrp0(xN,szszuzczcdt0(X459)))
| sbrdtbr0(X460) != xk
| ~ aSet0(X460)
| sdtlpdtrp0(xd,X459) = sdtlpdtrp0(sdtlpdtrp0(xC,X459),X460)
| ~ aElementOf0(X459,szNzAzT0) )
& ( ~ aElementOf0(X460,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X459)),xk))
| ~ aSet0(X460)
| sdtlpdtrp0(xd,X459) = sdtlpdtrp0(sdtlpdtrp0(xC,X459),X460)
| ~ aElementOf0(X459,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4730])])])])]) ).
fof(c_0_7,plain,
! [X387,X388] :
( ~ aFunction0(X387)
| ~ aElementOf0(X388,szDzozmdt0(X387))
| aElementOf0(sdtlpdtrp0(X387,X388),sdtlcdtrc0(X387,szDzozmdt0(X387))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgRng])])]) ).
cnf(c_0_8,hypothesis,
( aElementOf0(X1,szDzozmdt0(xd))
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,hypothesis,
szDzozmdt0(xd) = szNzAzT0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,hypothesis,
! [X462,X464,X465,X466] :
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ( aElementOf0(esk37_1(X462),szDzozmdt0(xd))
| ~ aElementOf0(X462,sdtlcdtrc0(xd,szDzozmdt0(xd))) )
& ( sdtlpdtrp0(xd,esk37_1(X462)) = X462
| ~ aElementOf0(X462,sdtlcdtrc0(xd,szDzozmdt0(xd))) )
& ( ~ aElementOf0(X465,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X465) != X464
| aElementOf0(X464,sdtlcdtrc0(xd,szDzozmdt0(xd))) )
& ( ~ aElementOf0(X466,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| aElementOf0(X466,xT) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),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__4758])])])])])]) ).
cnf(c_0_11,plain,
( aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1)))
| ~ aFunction0(X1)
| ~ aElementOf0(X2,szDzozmdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,hypothesis,
aFunction0(xd),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,hypothesis,
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,hypothesis,
aElementOf0(esk38_0,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_15,negated_conjecture,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_16,hypothesis,
( sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,hypothesis,
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,sdtlcdtrc0(xd,szDzozmdt0(xd))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,hypothesis,
( aElementOf0(sdtlpdtrp0(xd,X1),sdtlcdtrc0(xd,szNzAzT0))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_12])]) ).
cnf(c_0_19,hypothesis,
aElementOf0(esk38_0,szNzAzT0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,hypothesis,
szDzizrdt0(xd) = sdtlpdtrp0(xd,esk38_0),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_22,hypothesis,
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,sdtlcdtrc0(xd,szNzAzT0)) ),
inference(rw,[status(thm)],[c_0_17,c_0_9]) ).
cnf(c_0_23,hypothesis,
aElementOf0(sdtlpdtrp0(xd,esk38_0),sdtlcdtrc0(xd,szNzAzT0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xd,esk38_0),xT),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM597+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n025.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 00:49:28 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.19/3.51 % Version : CSE_E---1.7
% 4.19/3.51 % Problem : theBenchmark.p
% 4.19/3.51 % SZS status Theorem for theBenchmark.p
% 4.19/3.51 % SZS output start CNFRefutation
% See solution above
% 4.19/3.52 % Total time : 2.777s
%------------------------------------------------------------------------------