%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU294+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:45:43 AM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 23 ( 8 ~; 4 |; 6 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 14 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t13_finset_1,conjecture,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('theBenchmark.p',t13_finset_1) ).
fof(t13_finset_1_neg,negated_conjecture,
~ ! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
inference(assume_negation,[status(cth)],[t13_finset_1]) ).
cnf(c_114,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
fof(nnf_52,plain,
? [A,B] :
( ~ finite(A)
& finite(B)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t13_finset_1_neg]) ).
fof(sk_t13_finset_1_neg,plain,
( ~ finite(sK0)
& finite(sK1)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_52]) ).
cnf(c_117,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t13_finset_1_neg]) ).
cnf(c_118,negated_conjecture,
element(sK0,powerset(sK1)),
inference(resolve,[status(thm)],[c_117,c_114]) ).
cnf(c_120,negated_conjecture,
~ finite(sK0),
inference(split_conjunct,[status(thm)],[sk_t13_finset_1_neg]) ).
cnf(c_121,negated_conjecture,
finite(sK1),
inference(split_conjunct,[status(thm)],[sk_t13_finset_1_neg]) ).
cnf(c_167,plain,
( finite(B)
| ~ element(B,powerset(A))
| ~ finite(A) ),
inference(clausify,[status(thm)],[cc2_finset_1]) ).
cnf(c_209,negated_conjecture,
( finite(sK0)
| ~ finite(sK1) ),
inference(resolve,[status(thm)],[c_167,c_118]) ).
cnf(c_210,negated_conjecture,
finite(sK0),
inference(resolve,[status(thm)],[c_121,c_209]) ).
cnf(c_208,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_120,c_210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU294+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n019.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 09:07:18 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 933835 was started by sandbox on n019,
% 0.18/0.45 % Sat Sep 26 09:07:18 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 0.18/0.49
% 0.18/0.49 % SZS status Theorem for theBenchmark
% 0.18/0.49
% 0.18/0.49 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.18/0.49 % Length of proof is 10.
% 0.18/0.49 % Level of proof is 3.
% 0.18/0.49 % Maximum clause weight is 8.000.
% 0.18/0.49 % Given clauses 47.
% 0.18/0.49
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------