%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU189+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 : n017.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 2.66s 0.82s
% Output : CNFRefutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 80 ( 46 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 76 ( 31 ~; 31 |; 7 &)
% ( 2 <=>; 5 =>; 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(t60_relat_1,axiom,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('theBenchmark.p',t60_relat_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t65_relat_1,conjecture,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('theBenchmark.p',t65_relat_1) ).
fof(t65_relat_1_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
inference(assume_negation,[status(cth)],[t65_relat_1]) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
cnf(c_312,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc1_xboole_0]) ).
cnf(c_322,plain,
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(clausify,[status(thm)],[fc5_relat_1]) ).
cnf(c_323,plain,
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(clausify,[status(thm)],[fc6_relat_1]) ).
cnf(c_435,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[t60_relat_1]) ).
cnf(c_436,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[t60_relat_1]) ).
cnf(c_443,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
fof(nnf_169,plain,
? [A] :
( ( relation_rng(A) != empty_set
| relation_dom(A) != empty_set )
& ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
& relation(A) ),
inference(fof_nnf,[status(thm)],[t65_relat_1_neg]) ).
fof(sk_t65_relat_1_neg,plain,
( ( relation_rng(sK0) != empty_set
| relation_dom(sK0) != empty_set )
& ( relation_rng(sK0) = empty_set
| relation_dom(sK0) = empty_set )
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_169]) ).
cnf(c_457,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t65_relat_1_neg]) ).
cnf(c_458,negated_conjecture,
( relation_rng(sK0) = empty_set
| relation_dom(sK0) = empty_set ),
inference(split_conjunct,[status(thm)],[sk_t65_relat_1_neg]) ).
cnf(c_459,negated_conjecture,
( relation_rng(sK0) != empty_set
| relation_dom(sK0) != empty_set ),
inference(split_conjunct,[status(thm)],[sk_t65_relat_1_neg]) ).
cnf(c_2485,plain,
( ~ empty(empty_set)
| ~ relation(sK0)
| empty(sK0)
| relation_dom(sK0) = empty_set ),
inference(paramod,[status(thm)],[c_458,c_323]) ).
cnf(c_2486,negated_conjecture,
( ~ empty(empty_set)
| empty(sK0)
| relation_dom(sK0) = empty_set ),
inference(resolve,[status(thm)],[c_457,c_2485]) ).
cnf(c_2124,negated_conjecture,
( empty(sK0)
| relation_dom(sK0) = empty_set ),
inference(resolve,[status(thm)],[c_312,c_2486]) ).
cnf(c_2487,plain,
( empty_set = sK0
| relation_dom(sK0) = empty_set ),
inference(resolve,[status(thm)],[c_2124,c_443]) ).
cnf(c_2132,plain,
( sK0 = empty_set
| relation_dom(sK0) = empty_set ),
inference(copy,[status(thm)],[c_2487]) ).
cnf(c_2488,plain,
( ~ empty(empty_set)
| ~ relation(sK0)
| empty(sK0)
| sK0 = empty_set ),
inference(paramod,[status(thm)],[c_2132,c_322]) ).
cnf(c_2489,negated_conjecture,
( ~ empty(empty_set)
| empty(sK0)
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_457,c_2488]) ).
cnf(c_2415,negated_conjecture,
( empty(sK0)
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_312,c_2489]) ).
cnf(c_2490,plain,
( empty_set = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_2415,c_443]) ).
cnf(c_2491,plain,
( sK0 = empty_set
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_2490]) ).
cnf(c_2483,plain,
sK0 = empty_set,
inference(copy,[status(thm)],[c_2491]) ).
cnf(c_2492,negated_conjecture,
( relation_rng(sK0) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(paramod,[status(thm)],[c_2483,c_459]) ).
cnf(c_2493,negated_conjecture,
( relation_rng(sK0) != empty_set
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_435,c_2492]) ).
cnf(c_2494,negated_conjecture,
( relation_rng(empty_set) != empty_set
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_2483,c_2493]) ).
cnf(c_2495,negated_conjecture,
( empty_set != empty_set
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_436,c_2494]) ).
cnf(c_2496,negated_conjecture,
empty_set != empty_set,
inference(copy,[status(thm)],[c_2495]) ).
cnf(c_2484,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_2496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU189+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:42:48 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 302186 was started by sandbox2 on n017,
% 0.10/0.38 % Sat Sep 26 08:42:48 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.42
% 0.10/0.42 % From the command line: assign(max_seconds, 300).
% 0.10/0.42
% 0.10/0.42 % SInE: 137 to sos, 33 to usable, of 170 axioms (tolerance 2.00, depth 0 fixpoint).
% 2.66/0.82
% 2.66/0.82 % SZS status Theorem for theBenchmark
% 2.66/0.82
% 2.66/0.82 % Proof 1 at 0.31 (+ 0.07) seconds.
% 2.66/0.82 % Length of proof is 19.
% 2.66/0.82 % Level of proof is 6.
% 2.66/0.82 % Maximum clause weight is 18.000.
% 2.66/0.82 % Given clauses 242.
% 2.66/0.82
% 2.66/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------