%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU118+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 : n007.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 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 57 ( 3 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 51 ( 20 ~; 15 |; 5 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 31 ( 1 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_1) ).
fof(d5_finsub_1,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
file('theBenchmark.p',d5_finsub_1) ).
fof(dt_k5_finsub_1,axiom,
! [A] : preboolean(finite_subsets(A)),
file('theBenchmark.p',dt_k5_finsub_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t34_finsub_1,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ( finite(A)
=> element(B,finite_subsets(A)) ) ),
file('theBenchmark.p',t34_finsub_1) ).
fof(t34_finsub_1_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ( finite(A)
=> element(B,finite_subsets(A)) ) ),
inference(assume_negation,[status(cth)],[t34_finsub_1]) ).
cnf(c_38,plain,
( ~ finite(C)
| ~ subset(C,B)
| in(C,A)
| finite_subsets(B) != A
| ~ preboolean(A) ),
inference(clausify,[status(thm)],[d5_finsub_1]) ).
cnf(c_42,plain,
preboolean(finite_subsets(A)),
inference(clausify,[status(thm)],[dt_k5_finsub_1]) ).
cnf(c_79,plain,
( finite(B)
| ~ element(B,powerset(A))
| ~ finite(A) ),
inference(clausify,[status(thm)],[cc2_finset_1]) ).
cnf(c_108,plain,
( element(A,B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t1_subset]) ).
cnf(c_110,plain,
( subset(A,B)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
fof(nnf_32,plain,
? [A,B] :
( ~ element(B,finite_subsets(A))
& finite(A)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[t34_finsub_1_neg]) ).
fof(sk_t34_finsub_1_neg,plain,
( ~ element(sK0,finite_subsets(sK1))
& finite(sK1)
& element(sK0,powerset(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_32]) ).
cnf(c_117,negated_conjecture,
element(sK0,powerset(sK1)),
inference(split_conjunct,[status(thm)],[sk_t34_finsub_1_neg]) ).
cnf(c_118,negated_conjecture,
finite(sK1),
inference(split_conjunct,[status(thm)],[sk_t34_finsub_1_neg]) ).
cnf(c_119,negated_conjecture,
~ element(sK0,finite_subsets(sK1)),
inference(split_conjunct,[status(thm)],[sk_t34_finsub_1_neg]) ).
cnf(c_123,plain,
( ~ finite(C)
| ~ subset(C,A)
| in(C,finite_subsets(B))
| finite_subsets(A) != finite_subsets(B) ),
inference(resolve,[status(thm)],[c_42,c_38]) ).
cnf(c_239,plain,
subset(sK0,sK1),
inference(resolve,[status(thm)],[c_117,c_110]) ).
cnf(c_292,negated_conjecture,
( finite(sK0)
| ~ finite(sK1) ),
inference(resolve,[status(thm)],[c_117,c_79]) ).
cnf(c_241,negated_conjecture,
finite(sK0),
inference(resolve,[status(thm)],[c_118,c_292]) ).
cnf(c_245,negated_conjecture,
~ in(sK0,finite_subsets(sK1)),
inference(resolve,[status(thm)],[c_108,c_119]) ).
cnf(c_293,plain,
( ~ finite(A)
| ~ subset(A,B)
| in(A,finite_subsets(B)) ),
inference(xxres,[status(thm)],[c_123]) ).
cnf(c_294,plain,
( ~ finite(sK0)
| in(sK0,finite_subsets(sK1)) ),
inference(resolve,[status(thm)],[c_293,c_239]) ).
cnf(c_295,plain,
in(sK0,finite_subsets(sK1)),
inference(resolve,[status(thm)],[c_294,c_241]) ).
cnf(c_291,plain,
$false,
inference(resolve,[status(thm)],[c_245,c_295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU118+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:35:08 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3314936 was started by sandbox2 on n007,
% 0.09/0.36 % Sat Sep 26 08:35:08 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.42
% 0.14/0.42 % SZS status Theorem for theBenchmark
% 0.14/0.42
% 0.14/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.42 % Length of proof is 19.
% 0.14/0.42 % Level of proof is 3.
% 0.14/0.42 % Maximum clause weight is 24.000.
% 0.14/0.42 % Given clauses 72.
% 0.14/0.42
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------