%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU294+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 7.99s 1.76s
% Output : CNFRefutation 7.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% 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 : 15 ( 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_478,plain,
( finite(B)
| ~ element(B,powerset(A))
| ~ finite(A) ),
inference(clausify,[status(thm)],[cc2_finset_1]) ).
cnf(c_1870,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
fof(nnf_393,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_393]) ).
cnf(c_1989,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t13_finset_1_neg]) ).
cnf(c_1990,negated_conjecture,
finite(sK1),
inference(split_conjunct,[status(thm)],[sk_t13_finset_1_neg]) ).
cnf(c_1991,negated_conjecture,
~ finite(sK0),
inference(split_conjunct,[status(thm)],[sk_t13_finset_1_neg]) ).
cnf(c_2879,plain,
( finite(A)
| ~ element(A,powerset(sK1)) ),
inference(resolve,[status(thm)],[c_478,c_1990]) ).
cnf(c_3477,plain,
element(sK0,powerset(sK1)),
inference(resolve,[status(thm)],[c_1870,c_1989]) ).
cnf(c_3556,plain,
finite(sK0),
inference(resolve,[status(thm)],[c_3477,c_2879]) ).
cnf(c_3555,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1991,c_3556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU294+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n008.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 09:07:54 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3271686 was started by sandbox2 on n008,
% 0.09/0.35 % Sat Sep 26 09:07:54 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.23/0.55
% 0.23/0.55 % From the command line: assign(max_seconds, 300).
% 0.23/0.55
% 0.23/0.55 % SInE: 341 to sos, 53 to usable, of 394 axioms (tolerance 2.00, depth 0 fixpoint).
% 7.99/1.76
% 7.99/1.76 % SZS status Theorem for theBenchmark
% 7.99/1.76
% 7.99/1.76 % Proof 1 at 1.00 (+ 0.13) seconds.
% 7.99/1.76 % Length of proof is 11.
% 7.99/1.76 % Level of proof is 3.
% 7.99/1.76 % Maximum clause weight is 18.000.
% 7.99/1.76 % Given clauses 177.
% 7.99/1.76
% 7.99/1.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------