%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM549+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 : n023.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 04:57:47 PM UTC 2026
% Result : Theorem 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 65 ( 17 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 58 ( 22 ~; 16 |; 15 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 23 ( 1 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( aElement0(X1)
& aElementOf0(X1,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2270,hypothesis,
( aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,xS) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(mCardSeg,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sbrdtbr0(slbdtrb0(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSeg) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(c_0_8,negated_conjecture,
~ ? [X1] :
( aElement0(X1)
& aElementOf0(X1,xQ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_9,plain,
! [X124,X125] :
( ~ aSet0(X124)
| ~ aElementOf0(X125,X124)
| aElement0(X125) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_10,hypothesis,
! [X256] :
( aSet0(xQ)
& ( ~ aElementOf0(X256,xQ)
| aElementOf0(X256,xS) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2270])])]) ).
fof(c_0_11,negated_conjecture,
! [X257] :
( ~ aElement0(X257)
| ~ aElementOf0(X257,xQ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
cnf(c_0_12,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__2202_02]) ).
cnf(c_0_15,negated_conjecture,
( ~ aElement0(X1)
| ~ aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X126,X127,X128] :
( ( aSet0(X126)
| X126 != slcrc0 )
& ( ~ aElementOf0(X127,X126)
| X126 != slcrc0 )
& ( ~ aSet0(X128)
| aElementOf0(esk1_1(X128),X128)
| X128 = 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_17,hypothesis,
~ aElementOf0(X1,xQ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_18,plain,
( aElementOf0(esk1_1(X1),X1)
| X1 = slcrc0
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_20,plain,
! [X228] :
( ~ aElementOf0(X228,szNzAzT0)
| sbrdtbr0(slbdtrb0(X228)) = X228 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardSeg])]) ).
cnf(c_0_21,plain,
slbdtrb0(sz00) = slcrc0,
inference(split_conjunct,[status(thm)],[mSegZero]) ).
cnf(c_0_22,hypothesis,
slcrc0 = xQ,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_23,plain,
( sbrdtbr0(slbdtrb0(X1)) = X1
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
slbdtrb0(sz00) = xQ,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,hypothesis,
sbrdtbr0(xQ) = xk,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_27,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[m__2202_02]) ).
cnf(c_0_28,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM549+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 : n023.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 00:45:08 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Theorem for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.374s
%------------------------------------------------------------------------------