%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU085+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 : n010.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 0.14s 5.53s
% Output : CNFRefutation 0.14s
% 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(fc12_finset_1,axiom,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('theBenchmark.p',fc12_finset_1) ).
fof(t16_finset_1,conjecture,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('theBenchmark.p',t16_finset_1) ).
fof(t16_finset_1_neg,negated_conjecture,
~ ! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
inference(assume_negation,[status(cth)],[t16_finset_1]) ).
cnf(c_117,plain,
( finite(set_difference(A,B))
| ~ finite(A) ),
inference(clausify,[status(thm)],[fc12_finset_1]) ).
fof(nnf_58,plain,
? [A,B] :
( ~ finite(set_difference(A,B))
& finite(A) ),
inference(fof_nnf,[status(thm)],[t16_finset_1_neg]) ).
fof(sk_t16_finset_1_neg,plain,
( ~ finite(set_difference(sK0,sK1))
& finite(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_58]) ).
cnf(c_178,negated_conjecture,
finite(sK0),
inference(split_conjunct,[status(thm)],[sk_t16_finset_1_neg]) ).
cnf(c_179,negated_conjecture,
~ finite(set_difference(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t16_finset_1_neg]) ).
cnf(c_315,plain,
finite(set_difference(sK0,A)),
inference(resolve,[status(thm)],[c_178,c_117]) ).
cnf(c_316,plain,
$false,
inference(resolve,[status(thm)],[c_315,c_179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU085+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.42 % Computer : n010.cluster.edu
% 0.10/5.42 % Model : x86_64 x86_64
% 0.10/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.42 % Memory : 8046.5625MB
% 0.10/5.42 % OS : Linux 6.8.0-71-generic
% 0.10/5.42 % CPULimit : 300
% 0.10/5.42 % WCLimit : 300
% 0.10/5.42 % DateTime : Sat Sep 26 08:35:22 UTC 2026
% 0.10/5.42 % CPUTime :
% 0.10/5.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.43 % Process 2919709 was started by sandbox on n010,
% 0.10/5.43 % Sat Sep 26 08:35:22 2026
% 0.10/5.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.44
% 0.10/5.44 % From the command line: assign(max_seconds, 300).
% 0.14/5.53
% 0.14/5.53 % SZS status Theorem for theBenchmark
% 0.14/5.53
% 0.14/5.53 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/5.53 % Length of proof is 7.
% 0.14/5.53 % Level of proof is 3.
% 0.14/5.53 % Maximum clause weight is 16.000.
% 0.14/5.53 % Given clauses 71.
% 0.14/5.53
% 0.14/5.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------