%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM560+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 : n009.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 2.40s 2.03s
% Output : CNFRefutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 112 ( 15 equ)
% Maximal formula atoms : 39 ( 5 avg)
% Number of connectives : 154 ( 64 ~; 69 |; 14 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 41 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefPtt,axiom,
! [X1,X2] :
( ( aFunction0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtlbdtrb0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElementOf0(X4,szDzozmdt0(X1))
& sdtlpdtrp0(X1,X4) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPtt) ).
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(mDomSet,axiom,
! [X1] :
( aFunction0(X1)
=> aSet0(szDzozmdt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
fof(m__,conjecture,
aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2693,hypothesis,
( aFunction0(xF)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2693) ).
fof(c_0_5,plain,
! [X254,X255,X256,X257,X258,X259] :
( ( aSet0(X256)
| X256 != sdtlbdtrb0(X254,X255)
| ~ aFunction0(X254)
| ~ aElement0(X255) )
& ( aElementOf0(X257,szDzozmdt0(X254))
| ~ aElementOf0(X257,X256)
| X256 != sdtlbdtrb0(X254,X255)
| ~ aFunction0(X254)
| ~ aElement0(X255) )
& ( sdtlpdtrp0(X254,X257) = X255
| ~ aElementOf0(X257,X256)
| X256 != sdtlbdtrb0(X254,X255)
| ~ aFunction0(X254)
| ~ aElement0(X255) )
& ( ~ aElementOf0(X258,szDzozmdt0(X254))
| sdtlpdtrp0(X254,X258) != X255
| aElementOf0(X258,X256)
| X256 != sdtlbdtrb0(X254,X255)
| ~ aFunction0(X254)
| ~ aElement0(X255) )
& ( ~ aElementOf0(esk13_3(X254,X255,X259),X259)
| ~ aElementOf0(esk13_3(X254,X255,X259),szDzozmdt0(X254))
| sdtlpdtrp0(X254,esk13_3(X254,X255,X259)) != X255
| ~ aSet0(X259)
| X259 = sdtlbdtrb0(X254,X255)
| ~ aFunction0(X254)
| ~ aElement0(X255) )
& ( aElementOf0(esk13_3(X254,X255,X259),szDzozmdt0(X254))
| aElementOf0(esk13_3(X254,X255,X259),X259)
| ~ aSet0(X259)
| X259 = sdtlbdtrb0(X254,X255)
| ~ aFunction0(X254)
| ~ aElement0(X255) )
& ( sdtlpdtrp0(X254,esk13_3(X254,X255,X259)) = X255
| aElementOf0(esk13_3(X254,X255,X259),X259)
| ~ aSet0(X259)
| X259 = sdtlbdtrb0(X254,X255)
| ~ aFunction0(X254)
| ~ aElement0(X255) ) ),
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)],[mDefPtt])])])])])]) ).
cnf(c_0_6,plain,
( aElementOf0(X1,szDzozmdt0(X2))
| ~ aElementOf0(X1,X3)
| X3 != sdtlbdtrb0(X2,X4)
| ~ aFunction0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X134,X135,X136,X137] :
( ( aSet0(X135)
| ~ aSubsetOf0(X135,X134)
| ~ aSet0(X134) )
& ( ~ aElementOf0(X136,X135)
| aElementOf0(X136,X134)
| ~ aSubsetOf0(X135,X134)
| ~ aSet0(X134) )
& ( aElementOf0(esk2_2(X134,X137),X137)
| ~ aSet0(X137)
| aSubsetOf0(X137,X134)
| ~ aSet0(X134) )
& ( ~ aElementOf0(esk2_2(X134,X137),X134)
| ~ aSet0(X137)
| aSubsetOf0(X137,X134)
| ~ aSet0(X134) ) ),
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_8,plain,
( aSet0(X1)
| X1 != sdtlbdtrb0(X2,X3)
| ~ aFunction0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( aElementOf0(X1,szDzozmdt0(X2))
| ~ aFunction0(X2)
| ~ aElementOf0(X1,sdtlbdtrb0(X2,X3))
| ~ aElement0(X3) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( aSet0(sdtlbdtrb0(X1,X2))
| ~ aFunction0(X1)
| ~ aElement0(X2) ),
inference(er,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X251] :
( ~ aFunction0(X251)
| aSet0(szDzozmdt0(X251)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDomSet])]) ).
fof(c_0_13,negated_conjecture,
~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_14,plain,
( aSubsetOf0(X2,X1)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( aSubsetOf0(sdtlbdtrb0(X1,X2),X3)
| aElementOf0(esk2_2(X3,sdtlbdtrb0(X1,X2)),szDzozmdt0(X1))
| ~ aFunction0(X1)
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_16,plain,
( aSet0(szDzozmdt0(X1))
| ~ aFunction0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( aSubsetOf0(sdtlbdtrb0(X1,X2),szDzozmdt0(X1))
| ~ aFunction0(X1)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_11]) ).
cnf(c_0_19,hypothesis,
aFunction0(xF),
inference(split_conjunct,[status(thm)],[m__2693]) ).
cnf(c_0_20,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__2693]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM560+1 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % 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
% 0.16/0.35 % Computer : n009.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue May 5 00:44:41 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.20/0.36 % start to proof: theBenchmark
% 2.40/2.03 % Version : CSE_E---1.7
% 2.40/2.03 % Problem : theBenchmark.p
% 2.40/2.03 % SZS status Theorem for theBenchmark.p
% 2.40/2.03 % SZS output start CNFRefutation
% See solution above
% 2.40/2.04 % Total time : 1.374s
%------------------------------------------------------------------------------