%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM551+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:20:20 PM UTC 2026
% Result : Theorem 19.33s 3.03s
% Output : Proof 19.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 8 unt; 1 def)
% Number of atoms : 67 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 66 ( 28 ~; 22 |; 13 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 22 ( 0 sgn 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f4_nnf,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [W0,W1] :
( ( aElementOf0(sk0(W0),W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c6,plain,
( aElementOf0(sk0(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f65,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(f65_nnf,plain,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c133,plain,
aSet0(xQ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(p149,plain,
( aElementOf0(sk0(xQ),xQ)
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[c6,c133]) ).
fof(f2,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f2_nnf,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [W0,W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p142,plain,
( aElement0(X0)
| ~ aElementOf0(X0,xQ) ),
inference(resolution,[status(thm)],[c2,c133]) ).
cnf(p441,plain,
( aElement0(sk0(xQ))
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[p149,p142]) ).
fof(f67,conjecture,
? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f67_neg,negated_conjecture,
~ ? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f67]) ).
fof(f67_nnf,plain,
! [W0] :
( ~ aElementOf0(W0,xQ)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f67_neg]) ).
fof(f67_sk,plain,
! [W0] :
( ~ aElementOf0(W0,xQ)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c137,plain,
( ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(p442,plain,
( ~ aElementOf0(sk0(xQ),xQ)
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[p441,c137]) ).
cnf(p443,plain,
( xQ = slcrc0
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[p442,p149]) ).
cnf(p444,plain,
xQ = slcrc0,
inference(factoring,[status(thm)],[p443]) ).
fof(f66,hypothesis,
xQ != slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2313) ).
fof(f66_nnf,plain,
xQ != slcrc0,
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
xQ != slcrc0,
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c136,plain,
xQ != slcrc0,
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(p447,plain,
slcrc0 != slcrc0,
inference(demodulation,[status(thm)],[p444,c136]) ).
cnf(p448,plain,
$false,
inference(equality_resolution,[status(thm)],[p447]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM551+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 04:40:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 19.33/3.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.33/3.03 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------