%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU275+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 : 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 08:45:39 AM UTC 2026
% Result : Theorem 1.63s 0.73s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 62 ( 27 ~; 23 |; 6 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 21 ( 4 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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_630,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_709,plain,
relation(inclusion_relation(A)),
inference(clausify,[status(thm)],[dt_k1_wellord2]) ).
cnf(c_1012,plain,
reflexive(inclusion_relation(A)),
inference(clausify,[status(thm)],[t2_wellord2]) ).
cnf(c_1045,plain,
transitive(inclusion_relation(A)),
inference(clausify,[status(thm)],[t3_wellord2]) ).
cnf(c_1068,plain,
( connected(inclusion_relation(A))
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[t4_wellord2]) ).
cnf(c_1100,plain,
antisymmetric(inclusion_relation(A)),
inference(clausify,[status(thm)],[t5_wellord2]) ).
cnf(c_1119,plain,
( well_founded_relation(inclusion_relation(A))
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[t6_wellord2]) ).
fof(nnf_351,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_351]) ).
cnf(c_1148,negated_conjecture,
ordinal(sK0),
inference(split_conjunct,[status(thm)],[sk_t7_wellord2_neg]) ).
cnf(c_1149,negated_conjecture,
~ well_ordering(inclusion_relation(sK0)),
inference(split_conjunct,[status(thm)],[sk_t7_wellord2_neg]) ).
cnf(c_1531,plain,
connected(inclusion_relation(sK0)),
inference(resolve,[status(thm)],[c_1068,c_1148]) ).
cnf(c_1533,plain,
well_founded_relation(inclusion_relation(sK0)),
inference(resolve,[status(thm)],[c_1119,c_1148]) ).
cnf(c_2091,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_630,c_709]) ).
cnf(c_2092,plain,
( ~ well_founded_relation(inclusion_relation(A))
| ~ connected(inclusion_relation(A))
| ~ antisymmetric(inclusion_relation(A))
| ~ transitive(inclusion_relation(A))
| well_ordering(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_2091,c_1012]) ).
cnf(c_2093,plain,
( ~ well_founded_relation(inclusion_relation(A))
| ~ connected(inclusion_relation(A))
| ~ antisymmetric(inclusion_relation(A))
| well_ordering(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_2092,c_1045]) ).
cnf(c_2094,plain,
( ~ well_founded_relation(inclusion_relation(A))
| ~ connected(inclusion_relation(A))
| well_ordering(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_2093,c_1100]) ).
cnf(c_2095,plain,
( ~ well_founded_relation(inclusion_relation(sK0))
| well_ordering(inclusion_relation(sK0)) ),
inference(resolve,[status(thm)],[c_2094,c_1531]) ).
cnf(c_2096,plain,
well_ordering(inclusion_relation(sK0)),
inference(resolve,[status(thm)],[c_2095,c_1533]) ).
cnf(c_2090,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1149,c_2096]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU275+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 09:05:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1334681 was started by sandbox2 on n002,
% 0.13/0.36 % Sat Sep 26 09:05:21 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.45
% 0.13/0.45 % From the command line: assign(max_seconds, 300).
% 0.13/0.45
% 0.13/0.45 % SInE: 294 to sos, 58 to usable, of 352 axioms (tolerance 2.00, depth 0 fixpoint).
% 1.63/0.73
% 1.63/0.73 % SZS status Theorem for theBenchmark
% 1.63/0.73
% 1.63/0.73 % Proof 1 at 0.20 (+ 0.04) seconds.
% 1.63/0.73 % Length of proof is 20.
% 1.63/0.73 % Level of proof is 3.
% 1.63/0.73 % Maximum clause weight is 19.000.
% 1.63/0.73 % Given clauses 182.
% 1.63/0.73
% 1.63/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------