%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU295+1 : 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 : 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 08:45:43 AM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 3 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 2 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t13_finset_1,axiom,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('theBenchmark.p',t13_finset_1) ).
fof(t17_xboole_1,axiom,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_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_88,plain,
( finite(A)
| ~ finite(B)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t13_finset_1]) ).
cnf(c_90,plain,
subset(set_intersection2(A,B),A),
inference(clausify,[status(thm)],[t17_xboole_1]) ).
cnf(c_96,plain,
( finite(set_intersection2(A,B))
| ~ finite(A) ),
inference(resolve,[status(thm)],[c_90,c_88]) ).
fof(nnf_56,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_56]) ).
cnf(c_97,negated_conjecture,
~ finite(set_intersection2(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t15_finset_1_neg]) ).
cnf(c_98,negated_conjecture,
finite(sK0),
inference(split_conjunct,[status(thm)],[sk_t15_finset_1_neg]) ).
cnf(c_157,negated_conjecture,
~ finite(sK0),
inference(resolve,[status(thm)],[c_96,c_97]) ).
cnf(c_156,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_98,c_157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU295+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % 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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 09:04:53 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3374365 was started by sandbox2 on n007,
% 0.09/0.35 % Sat Sep 26 09:04:53 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 9.
% 0.09/0.38 % Level of proof is 3.
% 0.09/0.38 % Maximum clause weight is 6.000.
% 0.09/0.38 % Given clauses 5.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------