%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU261+2 : 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 : n003.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 08:45:37 AM UTC 2026
% Result : Theorem 14.16s 2.62s
% Output : CNFRefutation 14.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 71 ( 19 unt; 0 def)
% Number of atoms : 256 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 334 ( 149 ~; 141 |; 25 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 34 ( 0 sgn 10 !; 3 ?)
% 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(t53_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
=> ( ( well_founded_relation(A)
=> well_founded_relation(B) )
& ( antisymmetric(A)
=> antisymmetric(B) )
& ( connected(A)
=> connected(B) )
& ( transitive(A)
=> transitive(B) )
& ( reflexive(A)
=> reflexive(B) ) ) ) ) ) ),
file('theBenchmark.p',t53_wellord1) ).
fof(t54_wellord1,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_isomorphism(A,B,C)
& well_ordering(A) )
=> well_ordering(B) ) ) ) ),
file('theBenchmark.p',t54_wellord1) ).
fof(t54_wellord1_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_isomorphism(A,B,C)
& well_ordering(A) )
=> well_ordering(B) ) ) ) ),
inference(assume_negation,[status(cth)],[t54_wellord1]) ).
cnf(c_565,plain,
( reflexive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_566,plain,
( transitive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_567,plain,
( antisymmetric(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_568,plain,
( connected(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_569,plain,
( well_founded_relation(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_570,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_919,plain,
( reflexive(B)
| ~ reflexive(A)
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t53_wellord1]) ).
cnf(c_920,plain,
( transitive(B)
| ~ transitive(A)
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t53_wellord1]) ).
cnf(c_921,plain,
( connected(B)
| ~ connected(A)
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t53_wellord1]) ).
cnf(c_922,plain,
( antisymmetric(B)
| ~ antisymmetric(A)
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t53_wellord1]) ).
cnf(c_923,plain,
( well_founded_relation(B)
| ~ well_founded_relation(A)
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t53_wellord1]) ).
fof(nnf_319,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ well_ordering(B)
& relation_isomorphism(A,B,C)
& well_ordering(A)
& function(C)
& relation(C) )
& relation(B) )
& relation(A) ),
inference(fof_nnf,[status(thm)],[t54_wellord1_neg]) ).
fof(sk_t54_wellord1_neg,plain,
( ~ well_ordering(sK1)
& relation_isomorphism(sK0,sK1,sK2)
& well_ordering(sK0)
& function(sK2)
& relation(sK2)
& relation(sK1)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_319]) ).
cnf(c_990,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_991,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_992,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_993,negated_conjecture,
function(sK2),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_994,negated_conjecture,
well_ordering(sK0),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_995,negated_conjecture,
relation_isomorphism(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_996,negated_conjecture,
~ well_ordering(sK1),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_4297,negated_conjecture,
( reflexive(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_565,c_994]) ).
cnf(c_1227,negated_conjecture,
reflexive(sK0),
inference(resolve,[status(thm)],[c_990,c_4297]) ).
cnf(c_4298,negated_conjecture,
( transitive(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_566,c_994]) ).
cnf(c_1251,negated_conjecture,
transitive(sK0),
inference(resolve,[status(thm)],[c_990,c_4298]) ).
cnf(c_4299,negated_conjecture,
( antisymmetric(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_567,c_994]) ).
cnf(c_1252,negated_conjecture,
antisymmetric(sK0),
inference(resolve,[status(thm)],[c_990,c_4299]) ).
cnf(c_4300,negated_conjecture,
( connected(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_568,c_994]) ).
cnf(c_1253,negated_conjecture,
connected(sK0),
inference(resolve,[status(thm)],[c_990,c_4300]) ).
cnf(c_4301,negated_conjecture,
( well_founded_relation(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_569,c_994]) ).
cnf(c_1254,negated_conjecture,
well_founded_relation(sK0),
inference(resolve,[status(thm)],[c_990,c_4301]) ).
cnf(c_4302,negated_conjecture,
( reflexive(sK1)
| ~ reflexive(sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(sK1)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_919,c_995]) ).
cnf(c_4303,negated_conjecture,
( reflexive(sK1)
| ~ reflexive(sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_990,c_4302]) ).
cnf(c_4304,negated_conjecture,
( reflexive(sK1)
| ~ reflexive(sK0)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_991,c_4303]) ).
cnf(c_4305,negated_conjecture,
( reflexive(sK1)
| ~ reflexive(sK0)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_992,c_4304]) ).
cnf(c_4306,negated_conjecture,
( reflexive(sK1)
| ~ reflexive(sK0) ),
inference(resolve,[status(thm)],[c_993,c_4305]) ).
cnf(c_4270,negated_conjecture,
reflexive(sK1),
inference(resolve,[status(thm)],[c_1227,c_4306]) ).
cnf(c_4307,plain,
( ~ well_founded_relation(sK1)
| ~ connected(sK1)
| ~ antisymmetric(sK1)
| ~ transitive(sK1)
| well_ordering(sK1)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_4270,c_570]) ).
cnf(c_4308,negated_conjecture,
( ~ well_founded_relation(sK1)
| ~ connected(sK1)
| ~ antisymmetric(sK1)
| ~ transitive(sK1)
| well_ordering(sK1) ),
inference(resolve,[status(thm)],[c_991,c_4307]) ).
cnf(c_4271,negated_conjecture,
( ~ well_founded_relation(sK1)
| ~ connected(sK1)
| ~ antisymmetric(sK1)
| ~ transitive(sK1) ),
inference(resolve,[status(thm)],[c_996,c_4308]) ).
cnf(c_4309,negated_conjecture,
( transitive(sK1)
| ~ transitive(sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(sK1)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_920,c_995]) ).
cnf(c_4310,negated_conjecture,
( transitive(sK1)
| ~ transitive(sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_990,c_4309]) ).
cnf(c_4311,negated_conjecture,
( transitive(sK1)
| ~ transitive(sK0)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_991,c_4310]) ).
cnf(c_4312,negated_conjecture,
( transitive(sK1)
| ~ transitive(sK0)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_992,c_4311]) ).
cnf(c_4313,negated_conjecture,
( transitive(sK1)
| ~ transitive(sK0) ),
inference(resolve,[status(thm)],[c_993,c_4312]) ).
cnf(c_4272,negated_conjecture,
transitive(sK1),
inference(resolve,[status(thm)],[c_1251,c_4313]) ).
cnf(c_4273,negated_conjecture,
( ~ well_founded_relation(sK1)
| ~ connected(sK1)
| ~ antisymmetric(sK1) ),
inference(resolve,[status(thm)],[c_4272,c_4271]) ).
cnf(c_4314,negated_conjecture,
( connected(sK1)
| ~ connected(sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(sK1)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_921,c_995]) ).
cnf(c_4315,negated_conjecture,
( connected(sK1)
| ~ connected(sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_990,c_4314]) ).
cnf(c_4316,negated_conjecture,
( connected(sK1)
| ~ connected(sK0)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_991,c_4315]) ).
cnf(c_4317,negated_conjecture,
( connected(sK1)
| ~ connected(sK0)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_992,c_4316]) ).
cnf(c_4318,negated_conjecture,
( connected(sK1)
| ~ connected(sK0) ),
inference(resolve,[status(thm)],[c_993,c_4317]) ).
cnf(c_4283,negated_conjecture,
connected(sK1),
inference(resolve,[status(thm)],[c_1253,c_4318]) ).
cnf(c_4284,negated_conjecture,
( ~ well_founded_relation(sK1)
| ~ antisymmetric(sK1) ),
inference(resolve,[status(thm)],[c_4283,c_4273]) ).
cnf(c_4319,negated_conjecture,
( antisymmetric(sK1)
| ~ antisymmetric(sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(sK1)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_922,c_995]) ).
cnf(c_4320,negated_conjecture,
( antisymmetric(sK1)
| ~ antisymmetric(sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_990,c_4319]) ).
cnf(c_4321,negated_conjecture,
( antisymmetric(sK1)
| ~ antisymmetric(sK0)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_991,c_4320]) ).
cnf(c_4322,negated_conjecture,
( antisymmetric(sK1)
| ~ antisymmetric(sK0)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_992,c_4321]) ).
cnf(c_4323,negated_conjecture,
( antisymmetric(sK1)
| ~ antisymmetric(sK0) ),
inference(resolve,[status(thm)],[c_993,c_4322]) ).
cnf(c_4285,negated_conjecture,
antisymmetric(sK1),
inference(resolve,[status(thm)],[c_1252,c_4323]) ).
cnf(c_4286,negated_conjecture,
~ well_founded_relation(sK1),
inference(resolve,[status(thm)],[c_4285,c_4284]) ).
cnf(c_4324,negated_conjecture,
( well_founded_relation(sK1)
| ~ well_founded_relation(sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(sK1)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_923,c_995]) ).
cnf(c_4325,negated_conjecture,
( well_founded_relation(sK1)
| ~ well_founded_relation(sK0)
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_990,c_4324]) ).
cnf(c_4326,negated_conjecture,
( well_founded_relation(sK1)
| ~ well_founded_relation(sK0)
| ~ function(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_991,c_4325]) ).
cnf(c_4327,negated_conjecture,
( well_founded_relation(sK1)
| ~ well_founded_relation(sK0)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_992,c_4326]) ).
cnf(c_4328,negated_conjecture,
( well_founded_relation(sK1)
| ~ well_founded_relation(sK0) ),
inference(resolve,[status(thm)],[c_993,c_4327]) ).
cnf(c_4329,negated_conjecture,
well_founded_relation(sK1),
inference(resolve,[status(thm)],[c_1254,c_4328]) ).
cnf(c_4296,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_4286,c_4329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU261+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n003.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 09:02:24 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.41 % Process 2506442 was started by sandbox on n003,
% 0.15/0.41 % Sat Sep 26 09:02:24 2026
% 0.15/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.24/0.54
% 0.24/0.54 % From the command line: assign(max_seconds, 300).
% 0.24/0.54
% 0.24/0.54 % SInE: 274 to sos, 46 to usable, of 320 axioms (tolerance 2.00, depth 0 fixpoint).
% 14.16/2.62
% 14.16/2.62 % SZS status Theorem for theBenchmark
% 14.16/2.62
% 14.16/2.62 % Proof 1 at 1.68 (+ 0.28) seconds.
% 14.16/2.62 % Length of proof is 35.
% 14.16/2.62 % Level of proof is 8.
% 14.16/2.62 % Maximum clause weight is 21.000.
% 14.16/2.62 % Given clauses 369.
% 14.16/2.62
% 14.16/2.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------