%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU394+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 : n016.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 08:46:10 AM UTC 2026
% Result : Theorem 27.10s 4.41s
% Output : CNFRefutation 27.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 145 ( 17 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 176 ( 72 ~; 59 |; 35 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 29 ( 0 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc2_pre_topc,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(cast_as_carrier_subset(A)) ),
file('theBenchmark.p',fc2_pre_topc) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(t14_yellow19,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& ~ empty(B) )
=> set_difference(B,singleton(empty_set)) = filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)) ) ),
file('theBenchmark.p',t14_yellow19) ).
fof(t2_yellow19,axiom,
! [A] :
( ~ empty(A)
=> ! [B] :
( ( element(B,powerset(the_carrier(boole_POSet(A))))
& proper_element(B,powerset(the_carrier(boole_POSet(A))))
& upper_relstr_subset(B,boole_POSet(A))
& filtered_subset(B,boole_POSet(A))
& ~ empty(B) )
=> ! [C] :
~ ( empty(C)
& in(C,B) ) ) ),
file('theBenchmark.p',t2_yellow19) ).
fof(t65_zfmisc_1,axiom,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t15_yellow19,conjecture,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& ~ empty(B) )
=> B = filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)) ) ),
file('theBenchmark.p',t15_yellow19) ).
fof(t15_yellow19_neg,negated_conjecture,
~ ! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& ~ empty(B) )
=> B = filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)) ) ),
inference(assume_negation,[status(cth)],[t15_yellow19]) ).
fof(nnf_127,plain,
? [A] :
( ? [B] :
( filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)) != B
& element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& proper_element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
& upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
& ~ empty(B) )
& one_sorted_str(A)
& ~ empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t15_yellow19_neg]) ).
fof(sk_t15_yellow19_neg,plain,
( filter_of_net_str(sK0,net_of_bool_filter(sK0,cast_as_carrier_subset(sK0),sK1)) != sK1
& element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0)))))
& proper_element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0)))))
& upper_relstr_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0)))
& filtered_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0)))
& ~ empty(sK1)
& one_sorted_str(sK0)
& ~ empty_carrier(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_127]) ).
cnf(c_469,negated_conjecture,
filter_of_net_str(sK0,net_of_bool_filter(sK0,cast_as_carrier_subset(sK0),sK1)) != sK1,
inference(split_conjunct,[status(thm)],[sk_t15_yellow19_neg]) ).
cnf(c_470,negated_conjecture,
element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0))))),
inference(split_conjunct,[status(thm)],[sk_t15_yellow19_neg]) ).
cnf(c_471,negated_conjecture,
proper_element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0))))),
inference(split_conjunct,[status(thm)],[sk_t15_yellow19_neg]) ).
cnf(c_472,negated_conjecture,
upper_relstr_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0))),
inference(split_conjunct,[status(thm)],[sk_t15_yellow19_neg]) ).
cnf(c_473,negated_conjecture,
filtered_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0))),
inference(split_conjunct,[status(thm)],[sk_t15_yellow19_neg]) ).
cnf(c_474,negated_conjecture,
~ empty(sK1),
inference(split_conjunct,[status(thm)],[sk_t15_yellow19_neg]) ).
cnf(c_475,negated_conjecture,
one_sorted_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t15_yellow19_neg]) ).
cnf(c_476,negated_conjecture,
~ empty_carrier(sK0),
inference(split_conjunct,[status(thm)],[sk_t15_yellow19_neg]) ).
cnf(c_480,plain,
( in(B,A)
| set_difference(A,singleton(B)) = A ),
inference(clausify,[status(thm)],[t65_zfmisc_1]) ).
cnf(c_488,plain,
( ~ empty(C)
| ~ in(C,B)
| ~ element(B,powerset(the_carrier(boole_POSet(A))))
| ~ proper_element(B,powerset(the_carrier(boole_POSet(A))))
| ~ upper_relstr_subset(B,boole_POSet(A))
| ~ filtered_subset(B,boole_POSet(A))
| empty(B)
| empty(A) ),
inference(clausify,[status(thm)],[t2_yellow19]) ).
cnf(c_493,plain,
( set_difference(B,singleton(empty_set)) = filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B))
| ~ element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
| ~ upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
| ~ filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
| empty(B)
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[t14_yellow19]) ).
cnf(c_494,plain,
( filter_of_net_str(A,net_of_bool_filter(A,cast_as_carrier_subset(A),B)) = set_difference(B,singleton(empty_set))
| ~ element(B,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))
| ~ upper_relstr_subset(B,boole_POSet(cast_as_carrier_subset(A)))
| ~ filtered_subset(B,boole_POSet(cast_as_carrier_subset(A)))
| empty(B)
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(copy,[status(thm)],[c_493]) ).
cnf(c_630,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc4_relat_1]) ).
cnf(c_634,plain,
( ~ empty(cast_as_carrier_subset(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[fc2_pre_topc]) ).
cnf(c_9703,negated_conjecture,
( ~ empty(A)
| ~ in(A,sK1)
| ~ element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0)))))
| ~ upper_relstr_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0)))
| ~ filtered_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0)))
| empty(sK1)
| empty(cast_as_carrier_subset(sK0)) ),
inference(resolve,[status(thm)],[c_488,c_471]) ).
cnf(c_9704,negated_conjecture,
( ~ empty(A)
| ~ in(A,sK1)
| ~ element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0)))))
| ~ upper_relstr_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0)))
| ~ filtered_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0)))
| empty(cast_as_carrier_subset(sK0)) ),
inference(resolve,[status(thm)],[c_474,c_9703]) ).
cnf(c_9705,negated_conjecture,
( ~ empty(A)
| ~ in(A,sK1)
| ~ element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0)))))
| ~ upper_relstr_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0)))
| empty(cast_as_carrier_subset(sK0)) ),
inference(resolve,[status(thm)],[c_473,c_9704]) ).
cnf(c_9706,negated_conjecture,
( ~ empty(A)
| ~ in(A,sK1)
| ~ element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0)))))
| empty(cast_as_carrier_subset(sK0)) ),
inference(resolve,[status(thm)],[c_472,c_9705]) ).
cnf(c_2524,negated_conjecture,
( ~ empty(A)
| ~ in(A,sK1)
| empty(cast_as_carrier_subset(sK0)) ),
inference(resolve,[status(thm)],[c_470,c_9706]) ).
cnf(c_9707,negated_conjecture,
( filter_of_net_str(sK0,net_of_bool_filter(sK0,cast_as_carrier_subset(sK0),sK1)) = set_difference(sK1,singleton(empty_set))
| ~ element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0)))))
| ~ filtered_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0)))
| empty(sK1)
| ~ one_sorted_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_494,c_472]) ).
cnf(c_9708,negated_conjecture,
( filter_of_net_str(sK0,net_of_bool_filter(sK0,cast_as_carrier_subset(sK0),sK1)) = set_difference(sK1,singleton(empty_set))
| ~ element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0)))))
| ~ filtered_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0)))
| empty(sK1)
| ~ one_sorted_str(sK0) ),
inference(resolve,[status(thm)],[c_476,c_9707]) ).
cnf(c_9709,negated_conjecture,
( filter_of_net_str(sK0,net_of_bool_filter(sK0,cast_as_carrier_subset(sK0),sK1)) = set_difference(sK1,singleton(empty_set))
| ~ element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0)))))
| ~ filtered_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0)))
| empty(sK1) ),
inference(resolve,[status(thm)],[c_475,c_9708]) ).
cnf(c_9710,negated_conjecture,
( filter_of_net_str(sK0,net_of_bool_filter(sK0,cast_as_carrier_subset(sK0),sK1)) = set_difference(sK1,singleton(empty_set))
| ~ element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0)))))
| ~ filtered_subset(sK1,boole_POSet(cast_as_carrier_subset(sK0))) ),
inference(resolve,[status(thm)],[c_474,c_9709]) ).
cnf(c_9711,negated_conjecture,
( filter_of_net_str(sK0,net_of_bool_filter(sK0,cast_as_carrier_subset(sK0),sK1)) = set_difference(sK1,singleton(empty_set))
| ~ element(sK1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK0))))) ),
inference(resolve,[status(thm)],[c_473,c_9710]) ).
cnf(c_2541,negated_conjecture,
filter_of_net_str(sK0,net_of_bool_filter(sK0,cast_as_carrier_subset(sK0),sK1)) = set_difference(sK1,singleton(empty_set)),
inference(resolve,[status(thm)],[c_470,c_9711]) ).
cnf(c_6690,plain,
set_difference(sK1,singleton(empty_set)) != sK1,
inference(paramod,[status(thm)],[c_2541,c_469]) ).
cnf(c_6699,plain,
in(empty_set,sK1),
inference(resolve,[status(thm)],[c_6690,c_480]) ).
cnf(c_9712,plain,
( ~ empty(empty_set)
| empty(cast_as_carrier_subset(sK0)) ),
inference(resolve,[status(thm)],[c_6699,c_2524]) ).
cnf(c_6703,plain,
empty(cast_as_carrier_subset(sK0)),
inference(resolve,[status(thm)],[c_630,c_9712]) ).
cnf(c_9713,plain,
( ~ one_sorted_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_6703,c_634]) ).
cnf(c_9714,negated_conjecture,
~ one_sorted_str(sK0),
inference(resolve,[status(thm)],[c_476,c_9713]) ).
cnf(c_9702,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_475,c_9714]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU394+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 09:30:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 562161 was started by sandbox2 on n016,
% 0.09/0.37 % Sat Sep 26 09:30:32 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.41
% 0.09/0.41 % From the command line: assign(max_seconds, 300).
% 27.10/4.41
% 27.10/4.41 % given #500 (I,wt=72): 1155 empty_carrier(A) | -one_sorted_str(A) | empty(B) | -element(B,powerset(the_carrier(A))) | empty(C) | -filtered_subset(C,boole_POSet(B)) | -upper_relstr_subset(C,boole_POSet(B)) | -element(C,powerset(the_carrier(boole_POSet(B)))) | empty_carrier(net_of_bool_filter(A,B,C)) | -reflexive_relstr(net_of_bool_filter(A,B,C)) | -antisymmetric_relstr(net_of_bool_filter(A,B,C)) | -join_complete_relstr(net_of_bool_filter(A,B,C)) | with_infima_relstr(net_of_bool_filter(A,B,C)). [copy(1154),merge(i)].
% 27.10/4.41
% 27.10/4.41 % given #1000 (I,wt=13): 2149 -empty(f22(c10)). [copy(2148),unit_del(a,545),unit_del(b,543),unit_del(c,542)].
% 27.10/4.41
% 27.10/4.41 % given #1500 (W,wt=13): 3963 antisymmetric_relstr(f19(c4)). [resolve(1505,a,498,a)].
% 27.10/4.41
% 27.10/4.41 % SZS status Theorem for theBenchmark
% 27.10/4.41
% 27.10/4.41 % Proof 1 at 3.62 (+ 0.30) seconds.
% 27.10/4.41 % Length of proof is 26.
% 27.10/4.41 % Level of proof is 7.
% 27.10/4.41 % Maximum clause weight is 60.000.
% 27.10/4.41 % Given clauses 1597.
% 27.10/4.41
% 27.10/4.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------