%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU116+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:45:03 AM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 4 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 1 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 10 ( 1 sgn 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc3_finsub_1,axiom,
! [A,B] :
( element(B,finite_subsets(A))
=> finite(B) ),
file('theBenchmark.p',cc3_finsub_1) ).
fof(t30_finsub_1,conjecture,
! [A,B] :
( element(B,finite_subsets(A))
=> finite(B) ),
file('theBenchmark.p',t30_finsub_1) ).
fof(t30_finsub_1_neg,negated_conjecture,
~ ! [A,B] :
( element(B,finite_subsets(A))
=> finite(B) ),
inference(assume_negation,[status(cth)],[t30_finsub_1]) ).
cnf(c_61,plain,
( finite(A)
| ~ element(A,finite_subsets(B)) ),
inference(clausify,[status(thm)],[cc3_finsub_1]) ).
fof(nnf_30,plain,
? [A,B] :
( ~ finite(B)
& element(B,finite_subsets(A)) ),
inference(fof_nnf,[status(thm)],[t30_finsub_1_neg]) ).
fof(sk_t30_finsub_1_neg,plain,
( ~ finite(sK0)
& element(sK0,finite_subsets(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_30]) ).
cnf(c_80,negated_conjecture,
element(sK0,finite_subsets(sK1)),
inference(split_conjunct,[status(thm)],[sk_t30_finsub_1_neg]) ).
cnf(c_81,negated_conjecture,
~ finite(sK0),
inference(split_conjunct,[status(thm)],[sk_t30_finsub_1_neg]) ).
cnf(c_130,negated_conjecture,
finite(sK0),
inference(resolve,[status(thm)],[c_80,c_61]) ).
cnf(c_129,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_81,c_130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU116+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n003.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 08:38:53 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2463883 was started by sandbox2 on n003,
% 0.19/0.45 % Sat Sep 26 08:38:53 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 0.19/0.48
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48
% 0.19/0.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/0.48 % Length of proof is 6.
% 0.19/0.48 % Level of proof is 2.
% 0.19/0.48 % Maximum clause weight is 16.000.
% 0.19/0.48 % Given clauses 34.
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------