%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU188+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 : n012.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 08:45:21 AM UTC 2026
% Result : Theorem 0.07s 0.40s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 62 ( 28 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 54 ( 20 ~; 21 |; 6 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 9 ( 0 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_relat_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t64_relat_1,conjecture,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('theBenchmark.p',t64_relat_1) ).
fof(t64_relat_1_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
inference(assume_negation,[status(cth)],[t64_relat_1]) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
cnf(c_314,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc1_xboole_0]) ).
cnf(c_324,plain,
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(clausify,[status(thm)],[fc5_relat_1]) ).
cnf(c_325,plain,
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(clausify,[status(thm)],[fc6_relat_1]) ).
cnf(c_447,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
fof(nnf_168,plain,
? [A] :
( empty_set != A
& ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
& relation(A) ),
inference(fof_nnf,[status(thm)],[t64_relat_1_neg]) ).
fof(sk_t64_relat_1_neg,plain,
( empty_set != sK0
& ( relation_rng(sK0) = empty_set
| relation_dom(sK0) = empty_set )
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_168]) ).
cnf(c_461,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t64_relat_1_neg]) ).
cnf(c_462,negated_conjecture,
( relation_rng(sK0) = empty_set
| relation_dom(sK0) = empty_set ),
inference(split_conjunct,[status(thm)],[sk_t64_relat_1_neg]) ).
cnf(c_463,negated_conjecture,
empty_set != sK0,
inference(split_conjunct,[status(thm)],[sk_t64_relat_1_neg]) ).
cnf(c_464,negated_conjecture,
sK0 != empty_set,
inference(copy,[status(thm)],[c_463]) ).
cnf(c_943,plain,
( ~ empty(empty_set)
| ~ relation(sK0)
| empty(sK0)
| relation_dom(sK0) = empty_set ),
inference(paramod,[status(thm)],[c_462,c_325]) ).
cnf(c_944,negated_conjecture,
( ~ empty(empty_set)
| empty(sK0)
| relation_dom(sK0) = empty_set ),
inference(resolve,[status(thm)],[c_461,c_943]) ).
cnf(c_934,negated_conjecture,
( empty(sK0)
| relation_dom(sK0) = empty_set ),
inference(resolve,[status(thm)],[c_314,c_944]) ).
cnf(c_945,plain,
( empty_set = sK0
| relation_dom(sK0) = empty_set ),
inference(resolve,[status(thm)],[c_934,c_447]) ).
cnf(c_946,plain,
( sK0 = empty_set
| relation_dom(sK0) = empty_set ),
inference(copy,[status(thm)],[c_945]) ).
cnf(c_936,negated_conjecture,
relation_dom(sK0) = empty_set,
inference(resolve,[status(thm)],[c_464,c_946]) ).
cnf(c_947,plain,
( ~ empty(empty_set)
| ~ relation(sK0)
| empty(sK0) ),
inference(paramod,[status(thm)],[c_936,c_324]) ).
cnf(c_948,negated_conjecture,
( ~ empty(empty_set)
| empty(sK0) ),
inference(resolve,[status(thm)],[c_461,c_947]) ).
cnf(c_940,negated_conjecture,
empty(sK0),
inference(resolve,[status(thm)],[c_314,c_948]) ).
cnf(c_949,plain,
empty_set = sK0,
inference(resolve,[status(thm)],[c_940,c_447]) ).
cnf(c_950,plain,
sK0 = empty_set,
inference(copy,[status(thm)],[c_949]) ).
cnf(c_942,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_464,c_950]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU188+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 08:46:34 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.29 % Process 184389 was started by sandbox2 on n012,
% 0.02/0.29 % Sat Sep 26 08:46:34 2026
% 0.02/0.29 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.31
% 0.02/0.31 % From the command line: assign(max_seconds, 300).
% 0.02/0.31
% 0.02/0.31 % SInE: 142 to sos, 27 to usable, of 169 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.07/0.40
% 0.07/0.40 % SZS status Theorem for theBenchmark
% 0.07/0.40
% 0.07/0.40 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.07/0.40 % Length of proof is 16.
% 0.07/0.40 % Level of proof is 5.
% 0.07/0.40 % Maximum clause weight is 18.000.
% 0.07/0.40 % Given clauses 141.
% 0.07/0.40
% 0.07/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------