%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM531+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:17:18 AM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 37 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 37 ( 18 ~; 5 |; 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 : 9 ( 0 sgn 5 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCountNFin,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('theBenchmark.p',mCountNFin) ).
fof(m__,conjecture,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ ( W0 = slcrc0
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ ( W0 = slcrc0
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_12,plain,
( ~ isFinite0(A)
| ~ isCountable0(A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mCountNFin]) ).
fof(nnf_8,plain,
? [W0] :
( slcrc0 = W0
& ! [W1] : ~ aElementOf0(W1,W0)
& isCountable0(W0)
& aSet0(W0) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg,plain,
( slcrc0 = sK0
& ! [W1] : ~ aElementOf0(W1,sK0)
& isCountable0(sK0)
& aSet0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_8]) ).
cnf(c_13,negated_conjecture,
aSet0(sK0),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_14,negated_conjecture,
( ~ isFinite0(sK0)
| ~ isCountable0(sK0) ),
inference(resolve,[status(thm)],[c_13,c_12]) ).
cnf(c_16,negated_conjecture,
slcrc0 = sK0,
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_17,negated_conjecture,
sK0 = slcrc0,
inference(copy,[status(thm)],[c_16]) ).
cnf(c_20,negated_conjecture,
isCountable0(sK0),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_21,negated_conjecture,
isCountable0(slcrc0),
inference(paramod,[status(thm)],[c_17,c_20]) ).
fof(mEmpFin,axiom,
isFinite0(slcrc0),
file('theBenchmark.p',mEmpFin) ).
cnf(c_22,plain,
isFinite0(slcrc0),
inference(clausify,[status(thm)],[mEmpFin]) ).
cnf(c_25,negated_conjecture,
( ~ isFinite0(sK0)
| ~ isCountable0(slcrc0) ),
inference(paramod,[status(thm)],[c_17,c_14]) ).
cnf(c_26,negated_conjecture,
( ~ isFinite0(slcrc0)
| ~ isCountable0(slcrc0) ),
inference(paramod,[status(thm)],[c_17,c_25]) ).
cnf(c_27,negated_conjecture,
~ isFinite0(slcrc0),
inference(resolve,[status(thm)],[c_21,c_26]) ).
cnf(c_24,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_22,c_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM531+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 03:13:42 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 765771 was started by sandbox2 on n001,
% 0.10/0.36 % Sat Sep 26 03:13:42 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 11.
% 0.13/0.37 % Level of proof is 4.
% 0.13/0.37 % Maximum clause weight is 4.000.
% 0.13/0.37 % Given clauses 0.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------