%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU097+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:45:00 AM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 34 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 10 ~; 4 |; 7 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 4 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d6_xboole_0,axiom,
! [A,B] : symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
file('theBenchmark.p',d6_xboole_0) ).
fof(fc12_finset_1,axiom,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('theBenchmark.p',fc12_finset_1) ).
fof(fc9_finset_1,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
file('theBenchmark.p',fc9_finset_1) ).
fof(t28_finset_1,conjecture,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(symmetric_difference(A,B)) ),
file('theBenchmark.p',t28_finset_1) ).
fof(t28_finset_1_neg,negated_conjecture,
~ ! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(symmetric_difference(A,B)) ),
inference(assume_negation,[status(cth)],[t28_finset_1]) ).
cnf(c_125,plain,
symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
inference(clausify,[status(thm)],[d6_xboole_0]) ).
cnf(c_127,plain,
( finite(set_difference(A,B))
| ~ finite(A) ),
inference(clausify,[status(thm)],[fc12_finset_1]) ).
cnf(c_137,plain,
( finite(set_union2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(clausify,[status(thm)],[fc9_finset_1]) ).
fof(nnf_68,plain,
? [A,B] :
( ~ finite(symmetric_difference(A,B))
& finite(B)
& finite(A) ),
inference(fof_nnf,[status(thm)],[t28_finset_1_neg]) ).
fof(sk_t28_finset_1_neg,plain,
( ~ finite(symmetric_difference(sK0,sK1))
& finite(sK1)
& finite(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_68]) ).
cnf(c_195,negated_conjecture,
finite(sK0),
inference(split_conjunct,[status(thm)],[sk_t28_finset_1_neg]) ).
cnf(c_196,negated_conjecture,
finite(sK1),
inference(split_conjunct,[status(thm)],[sk_t28_finset_1_neg]) ).
cnf(c_197,negated_conjecture,
~ finite(symmetric_difference(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t28_finset_1_neg]) ).
cnf(c_198,negated_conjecture,
~ finite(set_union2(set_difference(sK0,sK1),set_difference(sK1,sK0))),
inference(paramod,[status(thm)],[c_125,c_197]) ).
cnf(c_371,plain,
finite(set_difference(sK0,A)),
inference(resolve,[status(thm)],[c_195,c_127]) ).
cnf(c_374,plain,
finite(set_difference(sK1,A)),
inference(resolve,[status(thm)],[c_196,c_127]) ).
cnf(c_530,plain,
( finite(set_union2(set_difference(sK0,B),A))
| ~ finite(A) ),
inference(resolve,[status(thm)],[c_137,c_371]) ).
cnf(c_531,negated_conjecture,
~ finite(set_difference(sK1,sK0)),
inference(resolve,[status(thm)],[c_530,c_198]) ).
cnf(c_529,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_374,c_531]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU097+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:36:03 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 866799 was started by sandbox on n019,
% 0.13/0.36 % Sat Sep 26 08:36:03 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 0.13/0.44
% 0.13/0.44 % SZS status Theorem for theBenchmark
% 0.13/0.44
% 0.13/0.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.13/0.44 % Length of proof is 14.
% 0.13/0.44 % Level of proof is 3.
% 0.13/0.44 % Maximum clause weight is 11.000.
% 0.13/0.44 % Given clauses 134.
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------