%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM549+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 : n029.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 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 61 ( 22 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 60 ( 24 ~; 21 |; 10 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 20 ( 0 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(m__,conjecture,
? [X1] :
( aElement0(X1)
& aElementOf0(X1,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2291,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(mCardEmpty,axiom,
! [X1] :
( aSet0(X1)
=> ( sbrdtbr0(X1) = sz00
<=> X1 = slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(c_0_6,plain,
! [X114,X115,X116] :
( ( aSet0(X114)
| X114 != slcrc0 )
& ( ~ aElementOf0(X115,X114)
| X114 != slcrc0 )
& ( ~ aSet0(X116)
| aElementOf0(esk1_1(X116),X116)
| X116 = 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])])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ? [X1] :
( aElement0(X1)
& aElementOf0(X1,xQ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,plain,
! [X112,X113] :
( ~ aSet0(X112)
| ~ aElementOf0(X113,X112)
| aElement0(X113) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_9,plain,
( aElementOf0(esk1_1(X1),X1)
| X1 = slcrc0
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
fof(c_0_11,negated_conjecture,
! [X230] :
( ~ aElement0(X230)
| ~ aElementOf0(X230,xQ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
cnf(c_0_12,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
( xQ = slcrc0
| aElementOf0(esk1_1(xQ),xQ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_14,plain,
! [X181] :
( ( sbrdtbr0(X181) != sz00
| X181 = slcrc0
| ~ aSet0(X181) )
& ( X181 != slcrc0
| sbrdtbr0(X181) = sz00
| ~ aSet0(X181) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardEmpty])])]) ).
cnf(c_0_15,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( ~ aElement0(X1)
| ~ aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
( xQ = slcrc0
| aElement0(esk1_1(xQ)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10])]) ).
cnf(c_0_18,plain,
( sbrdtbr0(X1) = sz00
| X1 != slcrc0
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_20,hypothesis,
sbrdtbr0(xQ) = xk,
inference(split_conjunct,[status(thm)],[m__2291]) ).
cnf(c_0_21,negated_conjecture,
xQ = slcrc0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_13]) ).
cnf(c_0_22,plain,
sbrdtbr0(slcrc0) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19])]) ).
cnf(c_0_23,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[m__2202_02]) ).
cnf(c_0_24,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM549+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 : n029.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 00:44:44 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------