%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU382+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 : n007.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 08:46:08 AM UTC 2026
% Result : Theorem 3.14s 0.86s
% Output : CNFRefutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 20 unt; 0 def)
% Number of atoms : 60 ( 28 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 43 ( 18 ~; 11 |; 9 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 41 ( 4 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(abstractness_v1_orders_2,axiom,
! [A] :
( rel_str(A)
=> ( strict_rel_str(A)
=> A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ),
file('theBenchmark.p',abstractness_v1_orders_2) ).
fof(d1_yellow_1,axiom,
! [A] : incl_POSet(A) = rel_str_of(A,inclusion_order(A)),
file('theBenchmark.p',d1_yellow_1) ).
fof(dt_k1_yellow_1,axiom,
! [A] :
( relation_of2_as_subset(inclusion_order(A),A,A)
& v1_partfun1(inclusion_order(A),A,A)
& transitive(inclusion_order(A))
& antisymmetric(inclusion_order(A))
& reflexive(inclusion_order(A)) ),
file('theBenchmark.p',dt_k1_yellow_1) ).
fof(dt_k2_yellow_1,axiom,
! [A] :
( rel_str(incl_POSet(A))
& strict_rel_str(incl_POSet(A)) ),
file('theBenchmark.p',dt_k2_yellow_1) ).
fof(fc5_yellow_1,axiom,
! [A] :
( antisymmetric_relstr(incl_POSet(A))
& transitive_relstr(incl_POSet(A))
& reflexive_relstr(incl_POSet(A))
& strict_rel_str(incl_POSet(A)) ),
file('theBenchmark.p',fc5_yellow_1) ).
fof(free_g1_orders_2,axiom,
! [A,B] :
( relation_of2(B,A,A)
=> ! [C,D] :
( rel_str_of(A,B) = rel_str_of(C,D)
=> ( B = D
& A = C ) ) ),
file('theBenchmark.p',free_g1_orders_2) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(t4_yellow_1,axiom,
! [A] : boole_POSet(A) = incl_POSet(powerset(A)),
file('theBenchmark.p',t4_yellow_1) ).
fof(t4_waybel_7,conjecture,
! [A] : the_carrier(boole_POSet(A)) = powerset(A),
file('theBenchmark.p',t4_waybel_7) ).
fof(t4_waybel_7_neg,negated_conjecture,
~ ! [A] : the_carrier(boole_POSet(A)) = powerset(A),
inference(assume_negation,[status(cth)],[t4_waybel_7]) ).
cnf(c_145,plain,
( rel_str_of(the_carrier(A),the_InternalRel(A)) = A
| ~ strict_rel_str(A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[abstractness_v1_orders_2]) ).
cnf(c_146,plain,
rel_str(incl_POSet(A)),
inference(clausify,[status(thm)],[dt_k2_yellow_1]) ).
cnf(c_161,plain,
relation_of2_as_subset(inclusion_order(A),A,A),
inference(clausify,[status(thm)],[dt_k1_yellow_1]) ).
cnf(c_163,plain,
( relation_of2(A,B,C)
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_219,plain,
relation_of2(inclusion_order(A),A,A),
inference(resolve,[status(thm)],[c_163,c_161]) ).
cnf(c_399,plain,
( rel_str_of(the_carrier(incl_POSet(A)),the_InternalRel(incl_POSet(A))) = incl_POSet(A)
| ~ strict_rel_str(incl_POSet(A)) ),
inference(resolve,[status(thm)],[c_146,c_145]) ).
fof(nnf_88,plain,
? [A] : powerset(A) != the_carrier(boole_POSet(A)),
inference(fof_nnf,[status(thm)],[t4_waybel_7_neg]) ).
fof(sk_t4_waybel_7_neg,plain,
powerset(sK0) != the_carrier(boole_POSet(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_88]) ).
cnf(c_475,negated_conjecture,
powerset(sK0) != the_carrier(boole_POSet(sK0)),
inference(split_conjunct,[status(thm)],[sk_t4_waybel_7_neg]) ).
cnf(c_476,negated_conjecture,
the_carrier(boole_POSet(sK0)) != powerset(sK0),
inference(copy,[status(thm)],[c_475]) ).
cnf(c_481,plain,
boole_POSet(A) = incl_POSet(powerset(A)),
inference(clausify,[status(thm)],[t4_yellow_1]) ).
cnf(c_569,plain,
( C = B
| rel_str_of(C,D) != rel_str_of(B,A)
| ~ relation_of2(A,B,B) ),
inference(clausify,[status(thm)],[free_g1_orders_2]) ).
cnf(c_624,plain,
strict_rel_str(incl_POSet(A)),
inference(clausify,[status(thm)],[fc5_yellow_1]) ).
cnf(c_647,plain,
incl_POSet(A) = rel_str_of(A,inclusion_order(A)),
inference(clausify,[status(thm)],[d1_yellow_1]) ).
cnf(c_1204,negated_conjecture,
the_carrier(incl_POSet(powerset(sK0))) != powerset(sK0),
inference(paramod,[status(thm)],[c_481,c_476]) ).
cnf(c_720,negated_conjecture,
the_carrier(rel_str_of(powerset(sK0),inclusion_order(powerset(sK0)))) != powerset(sK0),
inference(paramod,[status(thm)],[c_647,c_1204]) ).
cnf(c_1205,plain,
( rel_str_of(the_carrier(incl_POSet(A)),the_InternalRel(incl_POSet(A))) = incl_POSet(A)
| ~ strict_rel_str(rel_str_of(A,inclusion_order(A))) ),
inference(paramod,[status(thm)],[c_647,c_399]) ).
cnf(c_1206,plain,
( rel_str_of(the_carrier(rel_str_of(A,inclusion_order(A))),the_InternalRel(incl_POSet(A))) = incl_POSet(A)
| ~ strict_rel_str(rel_str_of(A,inclusion_order(A))) ),
inference(paramod,[status(thm)],[c_647,c_1205]) ).
cnf(c_1207,plain,
( rel_str_of(the_carrier(rel_str_of(A,inclusion_order(A))),the_InternalRel(rel_str_of(A,inclusion_order(A)))) = incl_POSet(A)
| ~ strict_rel_str(rel_str_of(A,inclusion_order(A))) ),
inference(paramod,[status(thm)],[c_647,c_1206]) ).
cnf(c_831,plain,
( rel_str_of(the_carrier(rel_str_of(A,inclusion_order(A))),the_InternalRel(rel_str_of(A,inclusion_order(A)))) = rel_str_of(A,inclusion_order(A))
| ~ strict_rel_str(rel_str_of(A,inclusion_order(A))) ),
inference(paramod,[status(thm)],[c_647,c_1207]) ).
cnf(c_834,plain,
strict_rel_str(rel_str_of(A,inclusion_order(A))),
inference(paramod,[status(thm)],[c_647,c_624]) ).
cnf(c_882,plain,
rel_str_of(the_carrier(rel_str_of(A,inclusion_order(A))),the_InternalRel(rel_str_of(A,inclusion_order(A)))) = rel_str_of(A,inclusion_order(A)),
inference(resolve,[status(thm)],[c_834,c_831]) ).
cnf(c_1208,plain,
( A = C
| rel_str_of(A,B) != rel_str_of(C,inclusion_order(C)) ),
inference(resolve,[status(thm)],[c_569,c_219]) ).
cnf(c_1202,plain,
the_carrier(rel_str_of(A,inclusion_order(A))) = A,
inference(resolve,[status(thm)],[c_1208,c_882]) ).
cnf(c_1203,plain,
$false,
inference(resolve,[status(thm)],[c_1202,c_720]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU382+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 09:21:24 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.37 % Process 3409210 was started by sandbox2 on n007,
% 0.13/0.37 % Sat Sep 26 09:21:24 2026
% 0.13/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.41
% 0.13/0.41 % From the command line: assign(max_seconds, 300).
% 3.14/0.86
% 3.14/0.86 % SZS status Theorem for theBenchmark
% 3.14/0.86
% 3.14/0.86 % Proof 1 at 0.36 (+ 0.06) seconds.
% 3.14/0.86 % Length of proof is 27.
% 3.14/0.86 % Level of proof is 6.
% 3.14/0.86 % Maximum clause weight is 46.000.
% 3.14/0.86 % Given clauses 392.
% 3.14/0.86
% 3.14/0.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------