%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /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 : Thu Sep 24 08:58:49 AM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : Proof 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(rc1_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal1) ).
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(f_1_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_1_2,plain,
! [U_0] :
( ( epsilon_connected(U_0)
& epsilon_transitive(U_0) )
| ~ ordinal(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( epsilon_transitive(U_0)
| ~ ordinal(U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( epsilon_connected(U_0)
| ~ ordinal(U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_2_2,plain,
! [U_1] :
( ordinal(U_1)
| ~ epsilon_connected(U_1)
| ~ epsilon_transitive(U_1) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ordinal(U_1)
| ~ epsilon_connected(U_1)
| ~ epsilon_transitive(U_1) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( ( ( well_ordering(A)
| ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A) )
& ( ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) )
| ~ well_ordering(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_wellord1]) ).
fof(f_3_2,plain,
! [U_2] :
( ( ( well_ordering(U_2)
| ~ well_founded_relation(U_2)
| ~ connected(U_2)
| ~ antisymmetric(U_2)
| ~ transitive(U_2)
| ~ reflexive(U_2) )
& ( ( well_founded_relation(U_2)
& connected(U_2)
& antisymmetric(U_2)
& transitive(U_2)
& reflexive(U_2) )
| ~ well_ordering(U_2) ) )
| ~ relation(U_2) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( reflexive(U_2)
| ~ well_ordering(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( transitive(U_2)
| ~ well_ordering(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_5,plain,
( antisymmetric(U_2)
| ~ well_ordering(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_6,plain,
( connected(U_2)
| ~ well_ordering(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_7,plain,
( well_founded_relation(U_2)
| ~ well_ordering(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_8,plain,
( well_ordering(U_2)
| ~ well_founded_relation(U_2)
| ~ connected(U_2)
| ~ antisymmetric(U_2)
| ~ transitive(U_2)
| ~ reflexive(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] : relation(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k1_wellord2]) ).
fof(f_4_2,plain,
! [U_3] : relation(inclusion_relation(U_3)),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
relation(inclusion_relation(U_3)),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_5_2,plain,
? [U_4] :
( ordinal(U_4)
& epsilon_connected(U_4)
& epsilon_transitive(U_4) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ordinal(sK1)
& epsilon_connected(sK1)
& epsilon_transitive(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_4,sK1)],[f_5_2]) ).
cnf(f_5_4,plain,
epsilon_transitive(sK1),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
epsilon_connected(sK1),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
ordinal(sK1),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] : reflexive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t2_wellord2]) ).
fof(f_6_2,plain,
! [U_5] : reflexive(inclusion_relation(U_5)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
reflexive(inclusion_relation(U_5)),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] : transitive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t3_wellord2]) ).
fof(f_7_2,plain,
! [U_6] : transitive(inclusion_relation(U_6)),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
transitive(inclusion_relation(U_6)),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( connected(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t4_wellord2]) ).
fof(f_8_2,plain,
! [U_7] :
( connected(inclusion_relation(U_7))
| ~ ordinal(U_7) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( connected(inclusion_relation(U_7))
| ~ ordinal(U_7) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] : antisymmetric(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t5_wellord2]) ).
fof(f_9_2,plain,
! [U_8] : antisymmetric(inclusion_relation(U_8)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
antisymmetric(inclusion_relation(U_8)),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] :
( well_founded_relation(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t6_wellord2]) ).
fof(f_10_2,plain,
! [U_9] :
( well_founded_relation(inclusion_relation(U_9))
| ~ ordinal(U_9) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( well_founded_relation(inclusion_relation(U_9))
| ~ ordinal(U_9) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
inference(negate,[status(cth)],[t7_wellord2]) ).
fof(f_11_2,negated_conjecture,
? [A] :
( ~ well_ordering(inclusion_relation(A))
& ordinal(A) ),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_10] :
( ~ well_ordering(inclusion_relation(U_10))
& ordinal(U_10) ),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
( ~ well_ordering(inclusion_relation(sK2))
& ordinal(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_10,sK2)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
( ~ well_ordering(inclusion_relation(sK2))
& ordinal(sK2) ),
inference(definitional_conversion,[status(esa)],[f_11_4]) ).
cnf(f_11_6,negated_conjecture,
ordinal(sK2),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_7,negated_conjecture,
~ well_ordering(inclusion_relation(sK2)),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 23:47:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------