%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU189+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 6 unt; 0 def)
% Number of atoms : 58 ( 49 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 56 ( 24 ~; 21 |; 5 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn 3 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t60_relat_1,axiom,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('theBenchmark.p',t60_relat_1) ).
fof(t64_relat_1,axiom,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('theBenchmark.p',t64_relat_1) ).
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]) ).
cnf(c_28,plain,
( empty_set = A
| relation_rng(A) != empty_set
| ~ relation(A) ),
inference(clausify,[status(thm)],[t64_relat_1]) ).
fof(nnf_24,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_24]) ).
cnf(c_29,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t65_relat_1_neg]) ).
cnf(c_30,plain,
( empty_set = A
| relation_dom(A) != empty_set
| ~ relation(A) ),
inference(clausify,[status(thm)],[t64_relat_1]) ).
cnf(c_67,negated_conjecture,
( empty_set = sK0
| relation_dom(sK0) != empty_set ),
inference(resolve,[status(thm)],[c_30,c_29]) ).
cnf(c_68,negated_conjecture,
( sK0 = empty_set
| relation_dom(sK0) != empty_set ),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_69,negated_conjecture,
( empty_set = sK0
| relation_rng(sK0) != empty_set ),
inference(resolve,[status(thm)],[c_28,c_29]) ).
cnf(c_70,negated_conjecture,
( sK0 = empty_set
| relation_rng(sK0) != empty_set ),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_82,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[t60_relat_1]) ).
cnf(c_83,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[t60_relat_1]) ).
cnf(c_84,negated_conjecture,
( relation_rng(sK0) = empty_set
| relation_dom(sK0) = empty_set ),
inference(split_conjunct,[status(thm)],[sk_t65_relat_1_neg]) ).
cnf(c_85,negated_conjecture,
( relation_rng(sK0) != empty_set
| relation_dom(sK0) != empty_set ),
inference(split_conjunct,[status(thm)],[sk_t65_relat_1_neg]) ).
cnf(c_109,plain,
( sK0 = empty_set
| relation_dom(sK0) = empty_set ),
inference(resolve,[status(thm)],[c_84,c_70]) ).
cnf(c_123,negated_conjecture,
( sK0 = empty_set
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_109,c_68]) ).
cnf(c_121,negated_conjecture,
sK0 = empty_set,
inference(copy,[status(thm)],[c_123]) ).
cnf(c_124,negated_conjecture,
( relation_rng(sK0) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(paramod,[status(thm)],[c_121,c_85]) ).
cnf(c_125,negated_conjecture,
( relation_rng(sK0) != empty_set
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_82,c_124]) ).
cnf(c_126,negated_conjecture,
( relation_rng(empty_set) != empty_set
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_121,c_125]) ).
cnf(c_127,negated_conjecture,
( empty_set != empty_set
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_83,c_126]) ).
cnf(c_128,negated_conjecture,
empty_set != empty_set,
inference(copy,[status(thm)],[c_127]) ).
cnf(c_122,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU189+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n002.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 08:50:05 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 1302155 was started by sandbox on n002,
% 0.16/0.43 % Sat Sep 26 08:50:05 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.47
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47
% 0.16/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/0.47 % Length of proof is 17.
% 0.16/0.47 % Level of proof is 6.
% 0.16/0.47 % Maximum clause weight is 8.000.
% 0.16/0.47 % Given clauses 37.
% 0.16/0.47
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------