%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU244+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 : n005.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 08:45:34 AM UTC 2026
% Result : Theorem 36.60s 5.83s
% Output : CNFRefutation 36.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 95 ( 15 unt; 0 def)
% Number of atoms : 263 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 284 ( 116 ~; 138 |; 12 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 39 ( 0 sgn 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d12_relat_2,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d12_relat_2) ).
fof(d14_relat_2,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d14_relat_2) ).
fof(d16_relat_2,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d16_relat_2) ).
fof(d4_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) ) ),
file('theBenchmark.p',d4_wellord1) ).
fof(d5_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( well_orders(A,B)
<=> ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) ) ) ),
file('theBenchmark.p',d5_wellord1) ).
fof(d9_relat_2,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d9_relat_2) ).
fof(t5_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('theBenchmark.p',t5_wellord1) ).
fof(t8_wellord1,conjecture,
! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
file('theBenchmark.p',t8_wellord1) ).
fof(t8_wellord1_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
inference(assume_negation,[status(cth)],[t8_wellord1]) ).
cnf(c_430,plain,
( is_antisymmetric_in(A,relation_field(A))
| ~ antisymmetric(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d12_relat_2]) ).
cnf(c_431,plain,
( ~ is_antisymmetric_in(A,relation_field(A))
| antisymmetric(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d12_relat_2]) ).
cnf(c_450,plain,
( is_connected_in(A,relation_field(A))
| ~ connected(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d14_relat_2]) ).
cnf(c_451,plain,
( ~ is_connected_in(A,relation_field(A))
| connected(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d14_relat_2]) ).
cnf(c_452,plain,
( is_transitive_in(A,relation_field(A))
| ~ transitive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d16_relat_2]) ).
cnf(c_453,plain,
( ~ is_transitive_in(A,relation_field(A))
| transitive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d16_relat_2]) ).
cnf(c_548,plain,
( reflexive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_549,plain,
( transitive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_550,plain,
( antisymmetric(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_551,plain,
( connected(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_552,plain,
( well_founded_relation(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_553,plain,
( ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A)
| well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_572,plain,
( is_reflexive_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_wellord1]) ).
cnf(c_573,plain,
( is_transitive_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_wellord1]) ).
cnf(c_574,plain,
( is_antisymmetric_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_wellord1]) ).
cnf(c_575,plain,
( is_connected_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_wellord1]) ).
cnf(c_576,plain,
( is_well_founded_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_wellord1]) ).
cnf(c_577,plain,
( ~ is_well_founded_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_antisymmetric_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_reflexive_in(A,B)
| well_orders(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_wellord1]) ).
cnf(c_617,plain,
( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d9_relat_2]) ).
cnf(c_618,plain,
( ~ is_reflexive_in(A,relation_field(A))
| reflexive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d9_relat_2]) ).
cnf(c_866,plain,
( is_well_founded_in(A,relation_field(A))
| ~ well_founded_relation(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t5_wellord1]) ).
cnf(c_867,plain,
( ~ is_well_founded_in(A,relation_field(A))
| well_founded_relation(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t5_wellord1]) ).
fof(nnf_297,plain,
? [A] :
( ( ~ well_ordering(A)
| ~ well_orders(A,relation_field(A)) )
& ( well_ordering(A)
| well_orders(A,relation_field(A)) )
& relation(A) ),
inference(fof_nnf,[status(thm)],[t8_wellord1_neg]) ).
fof(sk_t8_wellord1_neg,plain,
( ( ~ well_ordering(sK0)
| ~ well_orders(sK0,relation_field(sK0)) )
& ( well_ordering(sK0)
| well_orders(sK0,relation_field(sK0)) )
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_297]) ).
cnf(c_910,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t8_wellord1_neg]) ).
cnf(c_911,negated_conjecture,
( well_ordering(sK0)
| well_orders(sK0,relation_field(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_t8_wellord1_neg]) ).
cnf(c_912,negated_conjecture,
( ~ well_ordering(sK0)
| ~ well_orders(sK0,relation_field(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_t8_wellord1_neg]) ).
cnf(c_20780,negated_conjecture,
( is_well_founded_in(sK0,relation_field(sK0))
| ~ relation(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_911,c_576]) ).
cnf(c_1078,negated_conjecture,
( is_well_founded_in(sK0,relation_field(sK0))
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_910,c_20780]) ).
cnf(c_20781,negated_conjecture,
( is_connected_in(sK0,relation_field(sK0))
| ~ relation(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_911,c_575]) ).
cnf(c_1079,negated_conjecture,
( is_connected_in(sK0,relation_field(sK0))
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_910,c_20781]) ).
cnf(c_20782,negated_conjecture,
( is_antisymmetric_in(sK0,relation_field(sK0))
| ~ relation(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_911,c_574]) ).
cnf(c_1080,negated_conjecture,
( is_antisymmetric_in(sK0,relation_field(sK0))
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_910,c_20782]) ).
cnf(c_20783,negated_conjecture,
( is_transitive_in(sK0,relation_field(sK0))
| ~ relation(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_911,c_573]) ).
cnf(c_1081,negated_conjecture,
( is_transitive_in(sK0,relation_field(sK0))
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_910,c_20783]) ).
cnf(c_20784,negated_conjecture,
( is_reflexive_in(sK0,relation_field(sK0))
| ~ relation(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_911,c_572]) ).
cnf(c_1082,negated_conjecture,
( is_reflexive_in(sK0,relation_field(sK0))
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_910,c_20784]) ).
cnf(c_20785,plain,
( well_ordering(sK0)
| antisymmetric(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_431,c_1080]) ).
cnf(c_2334,negated_conjecture,
( well_ordering(sK0)
| antisymmetric(sK0) ),
inference(resolve,[status(thm)],[c_910,c_20785]) ).
cnf(c_20786,plain,
( antisymmetric(sK0)
| ~ relation(sK0)
| antisymmetric(sK0) ),
inference(resolve,[status(thm)],[c_2334,c_550]) ).
cnf(c_20787,plain,
( ~ relation(sK0)
| antisymmetric(sK0) ),
inference(copy,[status(thm)],[c_20786]) ).
cnf(c_2374,negated_conjecture,
antisymmetric(sK0),
inference(resolve,[status(thm)],[c_910,c_20787]) ).
cnf(c_20788,plain,
( is_antisymmetric_in(sK0,relation_field(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_2374,c_430]) ).
cnf(c_2375,negated_conjecture,
is_antisymmetric_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_910,c_20788]) ).
cnf(c_20789,plain,
( well_ordering(sK0)
| connected(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_451,c_1079]) ).
cnf(c_3163,negated_conjecture,
( well_ordering(sK0)
| connected(sK0) ),
inference(resolve,[status(thm)],[c_910,c_20789]) ).
cnf(c_20790,plain,
( well_ordering(sK0)
| transitive(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_453,c_1081]) ).
cnf(c_3164,negated_conjecture,
( well_ordering(sK0)
| transitive(sK0) ),
inference(resolve,[status(thm)],[c_910,c_20790]) ).
cnf(c_20791,plain,
( connected(sK0)
| ~ relation(sK0)
| connected(sK0) ),
inference(resolve,[status(thm)],[c_3163,c_551]) ).
cnf(c_20792,plain,
( ~ relation(sK0)
| connected(sK0) ),
inference(copy,[status(thm)],[c_20791]) ).
cnf(c_3169,negated_conjecture,
connected(sK0),
inference(resolve,[status(thm)],[c_910,c_20792]) ).
cnf(c_20793,plain,
( is_connected_in(sK0,relation_field(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_3169,c_450]) ).
cnf(c_3170,negated_conjecture,
is_connected_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_910,c_20793]) ).
cnf(c_20794,plain,
( transitive(sK0)
| ~ relation(sK0)
| transitive(sK0) ),
inference(resolve,[status(thm)],[c_3164,c_549]) ).
cnf(c_20795,plain,
( ~ relation(sK0)
| transitive(sK0) ),
inference(copy,[status(thm)],[c_20794]) ).
cnf(c_3172,negated_conjecture,
transitive(sK0),
inference(resolve,[status(thm)],[c_910,c_20795]) ).
cnf(c_20796,plain,
( is_transitive_in(sK0,relation_field(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_3172,c_452]) ).
cnf(c_3173,negated_conjecture,
is_transitive_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_910,c_20796]) ).
cnf(c_20797,plain,
( well_ordering(sK0)
| reflexive(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_618,c_1082]) ).
cnf(c_11588,negated_conjecture,
( well_ordering(sK0)
| reflexive(sK0) ),
inference(resolve,[status(thm)],[c_910,c_20797]) ).
cnf(c_20798,plain,
( reflexive(sK0)
| ~ relation(sK0)
| reflexive(sK0) ),
inference(resolve,[status(thm)],[c_11588,c_548]) ).
cnf(c_20799,plain,
( ~ relation(sK0)
| reflexive(sK0) ),
inference(copy,[status(thm)],[c_20798]) ).
cnf(c_11594,negated_conjecture,
reflexive(sK0),
inference(resolve,[status(thm)],[c_910,c_20799]) ).
cnf(c_20800,plain,
( is_reflexive_in(sK0,relation_field(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_11594,c_617]) ).
cnf(c_11595,negated_conjecture,
is_reflexive_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_910,c_20800]) ).
cnf(c_20801,plain,
( ~ well_founded_relation(sK0)
| ~ connected(sK0)
| ~ antisymmetric(sK0)
| ~ transitive(sK0)
| well_ordering(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_11594,c_553]) ).
cnf(c_20802,negated_conjecture,
( ~ well_founded_relation(sK0)
| ~ connected(sK0)
| ~ antisymmetric(sK0)
| ~ transitive(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_910,c_20801]) ).
cnf(c_20803,negated_conjecture,
( ~ well_founded_relation(sK0)
| ~ connected(sK0)
| ~ antisymmetric(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_3172,c_20802]) ).
cnf(c_20804,negated_conjecture,
( ~ well_founded_relation(sK0)
| ~ connected(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_2374,c_20803]) ).
cnf(c_11596,negated_conjecture,
( ~ well_founded_relation(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_3169,c_20804]) ).
cnf(c_20805,plain,
( ~ is_well_founded_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ is_transitive_in(sK0,relation_field(sK0))
| well_orders(sK0,relation_field(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_11595,c_577]) ).
cnf(c_20806,negated_conjecture,
( ~ is_well_founded_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ is_transitive_in(sK0,relation_field(sK0))
| well_orders(sK0,relation_field(sK0)) ),
inference(resolve,[status(thm)],[c_910,c_20805]) ).
cnf(c_20807,negated_conjecture,
( ~ is_well_founded_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| well_orders(sK0,relation_field(sK0)) ),
inference(resolve,[status(thm)],[c_3173,c_20806]) ).
cnf(c_20808,negated_conjecture,
( ~ is_well_founded_in(sK0,relation_field(sK0))
| ~ is_connected_in(sK0,relation_field(sK0))
| well_orders(sK0,relation_field(sK0)) ),
inference(resolve,[status(thm)],[c_2375,c_20807]) ).
cnf(c_11742,negated_conjecture,
( ~ is_well_founded_in(sK0,relation_field(sK0))
| well_orders(sK0,relation_field(sK0)) ),
inference(resolve,[status(thm)],[c_3170,c_20808]) ).
cnf(c_20809,plain,
( well_ordering(sK0)
| well_founded_relation(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_867,c_1078]) ).
cnf(c_20663,negated_conjecture,
( well_ordering(sK0)
| well_founded_relation(sK0) ),
inference(resolve,[status(thm)],[c_910,c_20809]) ).
cnf(c_20810,plain,
( well_founded_relation(sK0)
| ~ relation(sK0)
| well_founded_relation(sK0) ),
inference(resolve,[status(thm)],[c_20663,c_552]) ).
cnf(c_20811,plain,
( ~ relation(sK0)
| well_founded_relation(sK0) ),
inference(copy,[status(thm)],[c_20810]) ).
cnf(c_20775,negated_conjecture,
well_founded_relation(sK0),
inference(resolve,[status(thm)],[c_910,c_20811]) ).
cnf(c_20776,negated_conjecture,
well_ordering(sK0),
inference(resolve,[status(thm)],[c_20775,c_11596]) ).
cnf(c_20777,negated_conjecture,
~ well_orders(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_20776,c_912]) ).
cnf(c_20778,negated_conjecture,
~ is_well_founded_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_20777,c_11742]) ).
cnf(c_20812,plain,
( is_well_founded_in(sK0,relation_field(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_20775,c_866]) ).
cnf(c_20813,negated_conjecture,
is_well_founded_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_910,c_20812]) ).
cnf(c_20779,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_20778,c_20813]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU244+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n005.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 08:57:46 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 1766038 was started by sandbox2 on n005,
% 0.16/0.43 % Sat Sep 26 08:57:46 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.27/0.54
% 0.27/0.54 % From the command line: assign(max_seconds, 300).
% 0.27/0.54
% 0.27/0.54 % SInE: 245 to sos, 53 to usable, of 298 axioms (tolerance 2.00, depth 0 fixpoint).
% 36.60/5.83
% 36.60/5.83 % given #500 (F,wt=20): 5833 -in(f103(powerset(empty_set)),empty_set). [resolve(5823,a,1067,b)].
% 36.60/5.83
% 36.60/5.83 % given #1000 (W,wt=13): 12551 empty(function_inverse(empty_set)). [para(11532(a,1),12384(a,1))].
% 36.60/5.83
% 36.60/5.83 % given #1500 (F,wt=21): 15312 set_union2(c10,singleton(c10)) != empty_set. [para(454(a,1),15293(a,1))].
% 36.60/5.83
% 36.60/5.83 % SZS status Theorem for theBenchmark
% 36.60/5.83
% 36.60/5.83 % Proof 1 at 4.07 (+ 1.01) seconds.
% 36.60/5.83 % Length of proof is 58.
% 36.60/5.83 % Level of proof is 9.
% 36.60/5.83 % Maximum clause weight is 118.000.
% 36.60/5.83 % Given clauses 1897.
% 36.60/5.83
% 36.60/5.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
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