%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU083+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 : n009.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 08:44:59 AM UTC 2026
% Result : Theorem 0.20s 0.50s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 20 ( 7 ~; 3 |; 7 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 ( 0 sgn 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l3_finset_1,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
file('theBenchmark.p',l3_finset_1) ).
fof(t14_finset_1,conjecture,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
file('theBenchmark.p',t14_finset_1) ).
fof(t14_finset_1_neg,negated_conjecture,
~ ! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
inference(assume_negation,[status(cth)],[t14_finset_1]) ).
fof(nnf_60,plain,
? [A,B] :
( ~ finite(set_union2(A,B))
& finite(B)
& finite(A) ),
inference(fof_nnf,[status(thm)],[t14_finset_1_neg]) ).
fof(sk_t14_finset_1_neg,plain,
( ~ finite(set_union2(sK0,sK1))
& finite(sK1)
& finite(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_60]) ).
cnf(c_95,negated_conjecture,
~ finite(set_union2(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t14_finset_1_neg]) ).
cnf(c_96,negated_conjecture,
finite(sK1),
inference(split_conjunct,[status(thm)],[sk_t14_finset_1_neg]) ).
cnf(c_97,negated_conjecture,
finite(sK0),
inference(split_conjunct,[status(thm)],[sk_t14_finset_1_neg]) ).
cnf(c_98,plain,
( finite(set_union2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(clausify,[status(thm)],[l3_finset_1]) ).
cnf(c_187,negated_conjecture,
( finite(set_union2(sK0,A))
| ~ finite(A) ),
inference(resolve,[status(thm)],[c_98,c_97]) ).
cnf(c_188,negated_conjecture,
finite(set_union2(sK0,sK1)),
inference(resolve,[status(thm)],[c_187,c_96]) ).
cnf(c_186,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_95,c_188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU083+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n009.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sat Sep 26 08:35:00 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 3860129 was started by sandbox2 on n009,
% 0.20/0.46 % Sat Sep 26 08:35:00 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.48
% 0.20/0.48 % From the command line: assign(max_seconds, 300).
% 0.20/0.50
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50
% 0.20/0.50 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.20/0.50 % Length of proof is 7.
% 0.20/0.50 % Level of proof is 2.
% 0.20/0.50 % Maximum clause weight is 18.000.
% 0.20/0.50 % Given clauses 5.
% 0.20/0.50
% 0.20/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------