%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU244+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 : n009.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 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 95 ( 15 unt; 0 def)
% Number of atoms : 258 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 287 ( 124 ~; 133 |; 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 : 45 ( 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]) ).
fof(nnf_15,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_15]) ).
cnf(c_16,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t8_wellord1_neg]) ).
cnf(c_17,plain,
( ~ is_well_founded_in(A,relation_field(A))
| well_founded_relation(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t5_wellord1]) ).
cnf(c_18,plain,
( is_well_founded_in(A,relation_field(A))
| ~ well_founded_relation(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t5_wellord1]) ).
cnf(c_19,plain,
( ~ is_reflexive_in(A,relation_field(A))
| reflexive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d9_relat_2]) ).
cnf(c_20,plain,
( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d9_relat_2]) ).
cnf(c_22,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_23,plain,
( is_well_founded_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_wellord1]) ).
cnf(c_24,plain,
( is_connected_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_wellord1]) ).
cnf(c_25,plain,
( is_antisymmetric_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_wellord1]) ).
cnf(c_26,plain,
( is_transitive_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_wellord1]) ).
cnf(c_27,plain,
( is_reflexive_in(A,B)
| ~ well_orders(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_wellord1]) ).
cnf(c_28,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_29,plain,
( well_founded_relation(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_30,plain,
( connected(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_31,plain,
( antisymmetric(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_32,plain,
( transitive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_33,plain,
( reflexive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_34,plain,
( ~ is_transitive_in(A,relation_field(A))
| transitive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d16_relat_2]) ).
cnf(c_35,plain,
( is_transitive_in(A,relation_field(A))
| ~ transitive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d16_relat_2]) ).
cnf(c_36,plain,
( ~ is_connected_in(A,relation_field(A))
| connected(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d14_relat_2]) ).
cnf(c_37,plain,
( is_connected_in(A,relation_field(A))
| ~ connected(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d14_relat_2]) ).
cnf(c_38,plain,
( ~ is_antisymmetric_in(A,relation_field(A))
| antisymmetric(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d12_relat_2]) ).
cnf(c_39,plain,
( is_antisymmetric_in(A,relation_field(A))
| ~ antisymmetric(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d12_relat_2]) ).
cnf(c_40,negated_conjecture,
( is_antisymmetric_in(sK0,relation_field(sK0))
| ~ antisymmetric(sK0) ),
inference(resolve,[status(thm)],[c_16,c_39]) ).
cnf(c_41,negated_conjecture,
( ~ is_antisymmetric_in(sK0,relation_field(sK0))
| antisymmetric(sK0) ),
inference(resolve,[status(thm)],[c_16,c_38]) ).
cnf(c_42,negated_conjecture,
( is_connected_in(sK0,relation_field(sK0))
| ~ connected(sK0) ),
inference(resolve,[status(thm)],[c_16,c_37]) ).
cnf(c_43,negated_conjecture,
( ~ is_connected_in(sK0,relation_field(sK0))
| connected(sK0) ),
inference(resolve,[status(thm)],[c_16,c_36]) ).
cnf(c_44,negated_conjecture,
( is_transitive_in(sK0,relation_field(sK0))
| ~ transitive(sK0) ),
inference(resolve,[status(thm)],[c_16,c_35]) ).
cnf(c_45,negated_conjecture,
( ~ is_transitive_in(sK0,relation_field(sK0))
| transitive(sK0) ),
inference(resolve,[status(thm)],[c_16,c_34]) ).
cnf(c_46,negated_conjecture,
( reflexive(sK0)
| ~ well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_16,c_33]) ).
cnf(c_47,negated_conjecture,
( transitive(sK0)
| ~ well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_16,c_32]) ).
cnf(c_48,negated_conjecture,
( antisymmetric(sK0)
| ~ well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_16,c_31]) ).
cnf(c_49,negated_conjecture,
( connected(sK0)
| ~ well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_16,c_30]) ).
cnf(c_50,negated_conjecture,
( well_founded_relation(sK0)
| ~ well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_16,c_29]) ).
cnf(c_51,negated_conjecture,
( ~ well_founded_relation(sK0)
| ~ connected(sK0)
| ~ antisymmetric(sK0)
| ~ transitive(sK0)
| ~ reflexive(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_16,c_28]) ).
cnf(c_52,negated_conjecture,
( is_reflexive_in(sK0,A)
| ~ well_orders(sK0,A) ),
inference(resolve,[status(thm)],[c_16,c_27]) ).
cnf(c_53,negated_conjecture,
( is_transitive_in(sK0,A)
| ~ well_orders(sK0,A) ),
inference(resolve,[status(thm)],[c_16,c_26]) ).
cnf(c_54,negated_conjecture,
( is_antisymmetric_in(sK0,A)
| ~ well_orders(sK0,A) ),
inference(resolve,[status(thm)],[c_16,c_25]) ).
cnf(c_55,negated_conjecture,
( is_connected_in(sK0,A)
| ~ well_orders(sK0,A) ),
inference(resolve,[status(thm)],[c_16,c_24]) ).
cnf(c_56,negated_conjecture,
( is_well_founded_in(sK0,A)
| ~ well_orders(sK0,A) ),
inference(resolve,[status(thm)],[c_16,c_23]) ).
cnf(c_57,negated_conjecture,
( ~ is_well_founded_in(sK0,A)
| ~ is_connected_in(sK0,A)
| ~ is_antisymmetric_in(sK0,A)
| ~ is_transitive_in(sK0,A)
| ~ is_reflexive_in(sK0,A)
| well_orders(sK0,A) ),
inference(resolve,[status(thm)],[c_16,c_22]) ).
cnf(c_60,negated_conjecture,
( is_reflexive_in(sK0,relation_field(sK0))
| ~ reflexive(sK0) ),
inference(resolve,[status(thm)],[c_16,c_20]) ).
cnf(c_61,negated_conjecture,
( ~ is_reflexive_in(sK0,relation_field(sK0))
| reflexive(sK0) ),
inference(resolve,[status(thm)],[c_16,c_19]) ).
cnf(c_62,negated_conjecture,
( is_well_founded_in(sK0,relation_field(sK0))
| ~ well_founded_relation(sK0) ),
inference(resolve,[status(thm)],[c_16,c_18]) ).
cnf(c_63,negated_conjecture,
( ~ is_well_founded_in(sK0,relation_field(sK0))
| well_founded_relation(sK0) ),
inference(resolve,[status(thm)],[c_16,c_17]) ).
cnf(c_64,negated_conjecture,
( ~ well_ordering(sK0)
| ~ well_orders(sK0,relation_field(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_t8_wellord1_neg]) ).
cnf(c_65,negated_conjecture,
( well_ordering(sK0)
| well_orders(sK0,relation_field(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_t8_wellord1_neg]) ).
cnf(c_68,plain,
( is_well_founded_in(sK0,relation_field(sK0))
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_65,c_56]) ).
cnf(c_69,plain,
( is_connected_in(sK0,relation_field(sK0))
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_65,c_55]) ).
cnf(c_70,plain,
( is_antisymmetric_in(sK0,relation_field(sK0))
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_65,c_54]) ).
cnf(c_71,plain,
( is_transitive_in(sK0,relation_field(sK0))
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_65,c_53]) ).
cnf(c_72,plain,
( is_reflexive_in(sK0,relation_field(sK0))
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_65,c_52]) ).
cnf(c_74,plain,
( well_founded_relation(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_68,c_63]) ).
cnf(c_75,plain,
( connected(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_69,c_43]) ).
cnf(c_76,plain,
( antisymmetric(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_70,c_41]) ).
cnf(c_96,negated_conjecture,
( ~ connected(sK0)
| ~ antisymmetric(sK0)
| ~ transitive(sK0)
| ~ reflexive(sK0)
| well_ordering(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_74,c_51]) ).
cnf(c_77,negated_conjecture,
( ~ connected(sK0)
| ~ antisymmetric(sK0)
| ~ transitive(sK0)
| ~ reflexive(sK0)
| well_ordering(sK0) ),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_78,plain,
( transitive(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_71,c_45]) ).
cnf(c_97,plain,
( ~ connected(sK0)
| ~ antisymmetric(sK0)
| ~ reflexive(sK0)
| well_ordering(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_78,c_77]) ).
cnf(c_79,plain,
( ~ connected(sK0)
| ~ antisymmetric(sK0)
| ~ reflexive(sK0)
| well_ordering(sK0) ),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_80,plain,
( reflexive(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_72,c_61]) ).
cnf(c_98,plain,
( ~ connected(sK0)
| ~ antisymmetric(sK0)
| well_ordering(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_80,c_79]) ).
cnf(c_81,plain,
( ~ connected(sK0)
| ~ antisymmetric(sK0)
| well_ordering(sK0) ),
inference(copy,[status(thm)],[c_98]) ).
cnf(c_99,plain,
( well_ordering(sK0)
| ~ antisymmetric(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_81,c_75]) ).
cnf(c_82,plain,
( ~ antisymmetric(sK0)
| well_ordering(sK0) ),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_100,plain,
( well_ordering(sK0)
| well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_82,c_76]) ).
cnf(c_83,plain,
well_ordering(sK0),
inference(copy,[status(thm)],[c_100]) ).
cnf(c_84,negated_conjecture,
~ well_orders(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_83,c_64]) ).
cnf(c_85,negated_conjecture,
well_founded_relation(sK0),
inference(resolve,[status(thm)],[c_83,c_50]) ).
cnf(c_86,negated_conjecture,
connected(sK0),
inference(resolve,[status(thm)],[c_83,c_49]) ).
cnf(c_87,negated_conjecture,
antisymmetric(sK0),
inference(resolve,[status(thm)],[c_83,c_48]) ).
cnf(c_88,negated_conjecture,
transitive(sK0),
inference(resolve,[status(thm)],[c_83,c_47]) ).
cnf(c_89,negated_conjecture,
reflexive(sK0),
inference(resolve,[status(thm)],[c_83,c_46]) ).
cnf(c_90,negated_conjecture,
is_well_founded_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_85,c_62]) ).
cnf(c_91,negated_conjecture,
is_connected_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_86,c_42]) ).
cnf(c_92,negated_conjecture,
is_antisymmetric_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_87,c_40]) ).
cnf(c_93,negated_conjecture,
is_transitive_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_88,c_44]) ).
cnf(c_94,negated_conjecture,
is_reflexive_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_89,c_60]) ).
cnf(c_101,negated_conjecture,
( ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ is_transitive_in(sK0,relation_field(sK0))
| ~ is_reflexive_in(sK0,relation_field(sK0))
| well_orders(sK0,relation_field(sK0)) ),
inference(resolve,[status(thm)],[c_90,c_57]) ).
cnf(c_102,negated_conjecture,
( ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ is_transitive_in(sK0,relation_field(sK0))
| ~ is_reflexive_in(sK0,relation_field(sK0)) ),
inference(resolve,[status(thm)],[c_84,c_101]) ).
cnf(c_103,negated_conjecture,
( ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0))
| ~ is_transitive_in(sK0,relation_field(sK0)) ),
inference(resolve,[status(thm)],[c_94,c_102]) ).
cnf(c_104,negated_conjecture,
( ~ is_connected_in(sK0,relation_field(sK0))
| ~ is_antisymmetric_in(sK0,relation_field(sK0)) ),
inference(resolve,[status(thm)],[c_93,c_103]) ).
cnf(c_105,negated_conjecture,
~ is_connected_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_92,c_104]) ).
cnf(c_95,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_91,c_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU244+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n009.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 08:58:14 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 3916528 was started by sandbox on n009,
% 0.16/0.44 % Sat Sep 26 08:58:14 2026
% 0.16/0.44 % 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 0.00 (+ 0.00) seconds.
% 0.16/0.47 % Length of proof is 82.
% 0.16/0.47 % Level of proof is 12.
% 0.16/0.47 % Maximum clause weight is 23.000.
% 0.16/0.47 % Given clauses 50.
% 0.16/0.47
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------