%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM531+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 0.38s
% 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 : 33 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 14 ~; 5 |; 7 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 5 ( 0 sgn 3 !; 1 ?)
% 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 ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> W0 != slcrc0 ),
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
& isCountable0(W0)
& aSet0(W0) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg,plain,
( slcrc0 = 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_18,negated_conjecture,
isCountable0(sK0),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_19,negated_conjecture,
isCountable0(slcrc0),
inference(paramod,[status(thm)],[c_17,c_18]) ).
fof(mEmpFin,axiom,
isFinite0(slcrc0),
file('theBenchmark.p',mEmpFin) ).
cnf(c_20,plain,
isFinite0(slcrc0),
inference(clausify,[status(thm)],[mEmpFin]) ).
cnf(c_22,negated_conjecture,
( ~ isFinite0(sK0)
| ~ isCountable0(slcrc0) ),
inference(paramod,[status(thm)],[c_17,c_14]) ).
cnf(c_23,negated_conjecture,
( ~ isFinite0(slcrc0)
| ~ isCountable0(slcrc0) ),
inference(paramod,[status(thm)],[c_17,c_22]) ).
cnf(c_24,negated_conjecture,
~ isFinite0(slcrc0),
inference(resolve,[status(thm)],[c_19,c_23]) ).
cnf(c_21,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_20,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM531+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.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 : Sat Sep 26 03:07:29 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3657734 was started by sandbox on n011,
% 0.13/0.36 % Sat Sep 26 03:07:29 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 11.
% 0.13/0.38 % Level of proof is 4.
% 0.13/0.38 % Maximum clause weight is 4.000.
% 0.13/0.38 % Given clauses 0.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------