%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU295+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 : n026.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 6.55s 1.74s
% Output : CNFRefutation 6.55s
% 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 : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 2 sgn 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc11_finset_1,axiom,
! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
file('theBenchmark.p',fc11_finset_1) ).
fof(t15_finset_1,conjecture,
! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
file('theBenchmark.p',t15_finset_1) ).
fof(t15_finset_1_neg,negated_conjecture,
~ ! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
inference(assume_negation,[status(cth)],[t15_finset_1]) ).
cnf(c_802,plain,
( finite(set_intersection2(A,B))
| ~ finite(A) ),
inference(clausify,[status(thm)],[fc11_finset_1]) ).
fof(nnf_396,plain,
? [A,B] :
( ~ finite(set_intersection2(A,B))
& finite(A) ),
inference(fof_nnf,[status(thm)],[t15_finset_1_neg]) ).
fof(sk_t15_finset_1_neg,plain,
( ~ finite(set_intersection2(sK0,sK1))
& finite(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_396]) ).
cnf(c_1961,negated_conjecture,
finite(sK0),
inference(split_conjunct,[status(thm)],[sk_t15_finset_1_neg]) ).
cnf(c_1962,negated_conjecture,
~ finite(set_intersection2(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t15_finset_1_neg]) ).
cnf(c_2865,plain,
finite(set_intersection2(sK0,A)),
inference(resolve,[status(thm)],[c_802,c_1961]) ).
cnf(c_2866,plain,
$false,
inference(resolve,[status(thm)],[c_2865,c_1962]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU295+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n026.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Sat Sep 26 09:09:55 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 628192 was started by sandbox2 on n026,
% 0.20/0.45 % Sat Sep 26 09:09:55 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.57/0.80
% 0.57/0.80 % From the command line: assign(max_seconds, 300).
% 0.57/0.80
% 0.57/0.80 % SInE: 341 to sos, 56 to usable, of 397 axioms (tolerance 2.00, depth 0 fixpoint).
% 6.55/1.74
% 6.55/1.74 % SZS status Theorem for theBenchmark
% 6.55/1.74
% 6.55/1.74 % Proof 1 at 0.75 (+ 0.08) seconds.
% 6.55/1.74 % Length of proof is 7.
% 6.55/1.74 % Level of proof is 3.
% 6.55/1.74 % Maximum clause weight is 16.000.
% 6.55/1.74 % Given clauses 52.
% 6.55/1.74
% 6.55/1.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------