%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM531+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 02:20:16 PM UTC 2026
% Result : Theorem 3.75s 0.99s
% Output : Proof 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 39 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 41 ( 20 ~; 7 |; 11 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 11 ( 0 sgn 7 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
fof(f7_nnf,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f8,conjecture,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ ( W0 = slcrc0
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f8_neg,negated_conjecture,
~ ! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ ( W0 = slcrc0
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [W0] :
( W0 = slcrc0
& ! [W1] : ~ aElementOf0(W1,W0)
& isCountable0(W0)
& aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
! [W1] :
( sk1 = slcrc0
& ~ aElementOf0(W1,sk1)
& isCountable0(sk1)
& aSet0(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f8_nnf]) ).
cnf(c10,plain,
aSet0(sk1),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p18,plain,
( ~ isFinite0(slcrc0)
| ~ isCountable0(slcrc0) ),
inference(resolution,[status(thm)],[c9,c10]) ).
cnf(c13,plain,
sk1 = slcrc0,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(c11,plain,
isCountable0(sk1),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p16,plain,
isCountable0(slcrc0),
inference(superposition,[status(thm)],[c13,c11]) ).
cnf(p19,plain,
~ isFinite0(slcrc0),
inference(resolution,[status(thm)],[p18,p16]) ).
fof(f5,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
fof(f5_nnf,plain,
isFinite0(slcrc0),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c7,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(p20,plain,
$false,
inference(resolution,[status(thm)],[p19,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM531+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 04:32:13 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.75/0.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.75/0.99 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------