%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU275+1 : 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 : n026.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 08:45:39 AM UTC 2026
% Result : Theorem 0.18s 0.46s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 16 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 85 ( 39 ~; 30 |; 8 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 24 ( 4 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
fof(cc2_ordinal1,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('theBenchmark.p',cc2_ordinal1) ).
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(dt_k1_wellord2,axiom,
! [A] : relation(inclusion_relation(A)),
file('theBenchmark.p',dt_k1_wellord2) ).
fof(t2_wellord2,axiom,
! [A] : reflexive(inclusion_relation(A)),
file('theBenchmark.p',t2_wellord2) ).
fof(t3_wellord2,axiom,
! [A] : transitive(inclusion_relation(A)),
file('theBenchmark.p',t3_wellord2) ).
fof(t4_wellord2,axiom,
! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ),
file('theBenchmark.p',t4_wellord2) ).
fof(t5_wellord2,axiom,
! [A] : antisymmetric(inclusion_relation(A)),
file('theBenchmark.p',t5_wellord2) ).
fof(t6_wellord2,axiom,
! [A] :
( ordinal(A)
=> well_founded_relation(inclusion_relation(A)) ),
file('theBenchmark.p',t6_wellord2) ).
fof(t7_wellord2,conjecture,
! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
file('theBenchmark.p',t7_wellord2) ).
fof(t7_wellord2_neg,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
inference(assume_negation,[status(cth)],[t7_wellord2]) ).
cnf(c_12,plain,
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(clausify,[status(thm)],[cc2_ordinal1]) ).
cnf(c_13,plain,
( epsilon_connected(A)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[cc1_ordinal1]) ).
cnf(c_14,plain,
( epsilon_transitive(A)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[cc1_ordinal1]) ).
cnf(c_16,plain,
( connected(inclusion_relation(A))
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[t4_wellord2]) ).
cnf(c_17,plain,
( well_founded_relation(inclusion_relation(A))
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[t6_wellord2]) ).
fof(nnf_11,plain,
? [A] :
( ~ well_ordering(inclusion_relation(A))
& ordinal(A) ),
inference(fof_nnf,[status(thm)],[t7_wellord2_neg]) ).
fof(sk_t7_wellord2_neg,plain,
( ~ well_ordering(inclusion_relation(sK0))
& ordinal(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_11]) ).
cnf(c_18,negated_conjecture,
ordinal(sK0),
inference(split_conjunct,[status(thm)],[sk_t7_wellord2_neg]) ).
cnf(c_19,plain,
( ~ epsilon_connected(A)
| ~ epsilon_transitive(A)
| well_founded_relation(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_17,c_12]) ).
cnf(c_20,negated_conjecture,
epsilon_transitive(sK0),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_25,negated_conjecture,
( ~ epsilon_connected(sK0)
| well_founded_relation(inclusion_relation(sK0)) ),
inference(resolve,[status(thm)],[c_19,c_20]) ).
cnf(c_30,negated_conjecture,
epsilon_connected(sK0),
inference(resolve,[status(thm)],[c_18,c_13]) ).
cnf(c_31,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_32,plain,
relation(inclusion_relation(A)),
inference(clausify,[status(thm)],[dt_k1_wellord2]) ).
cnf(c_38,plain,
( ~ well_founded_relation(inclusion_relation(A))
| ~ connected(inclusion_relation(A))
| ~ antisymmetric(inclusion_relation(A))
| ~ transitive(inclusion_relation(A))
| ~ reflexive(inclusion_relation(A))
| well_ordering(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_31,c_32]) ).
cnf(c_44,negated_conjecture,
~ well_ordering(inclusion_relation(sK0)),
inference(split_conjunct,[status(thm)],[sk_t7_wellord2_neg]) ).
cnf(c_45,plain,
reflexive(inclusion_relation(A)),
inference(clausify,[status(thm)],[t2_wellord2]) ).
cnf(c_46,negated_conjecture,
( ~ well_founded_relation(inclusion_relation(sK0))
| ~ connected(inclusion_relation(sK0))
| ~ antisymmetric(inclusion_relation(sK0))
| ~ transitive(inclusion_relation(sK0))
| ~ reflexive(inclusion_relation(sK0)) ),
inference(resolve,[status(thm)],[c_44,c_38]) ).
cnf(c_47,plain,
transitive(inclusion_relation(A)),
inference(clausify,[status(thm)],[t3_wellord2]) ).
cnf(c_48,negated_conjecture,
( ~ well_founded_relation(inclusion_relation(sK0))
| ~ connected(inclusion_relation(sK0))
| ~ antisymmetric(inclusion_relation(sK0))
| ~ transitive(inclusion_relation(sK0)) ),
inference(resolve,[status(thm)],[c_45,c_46]) ).
cnf(c_49,plain,
antisymmetric(inclusion_relation(A)),
inference(clausify,[status(thm)],[t5_wellord2]) ).
cnf(c_50,negated_conjecture,
( ~ well_founded_relation(inclusion_relation(sK0))
| ~ connected(inclusion_relation(sK0))
| ~ antisymmetric(inclusion_relation(sK0)) ),
inference(resolve,[status(thm)],[c_47,c_48]) ).
cnf(c_52,negated_conjecture,
( ~ well_founded_relation(inclusion_relation(sK0))
| ~ connected(inclusion_relation(sK0)) ),
inference(resolve,[status(thm)],[c_49,c_50]) ).
cnf(c_53,negated_conjecture,
connected(inclusion_relation(sK0)),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_55,negated_conjecture,
well_founded_relation(inclusion_relation(sK0)),
inference(resolve,[status(thm)],[c_30,c_25]) ).
cnf(c_56,negated_conjecture,
~ well_founded_relation(inclusion_relation(sK0)),
inference(resolve,[status(thm)],[c_53,c_52]) ).
cnf(c_59,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_55,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n026.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 09:05:40 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 613837 was started by sandbox2 on n026,
% 0.18/0.44 % Sat Sep 26 09:05:40 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.46
% 0.18/0.46 % SZS status Theorem for theBenchmark
% 0.18/0.46
% 0.18/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.46 % Length of proof is 35.
% 0.18/0.46 % Level of proof is 8.
% 0.18/0.46 % Maximum clause weight is 0.000.
% 0.18/0.46 % Given clauses 0.
% 0.18/0.46
% 0.18/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------