%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU394+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:12:09 PM UTC 2026
% Result : Theorem 1.48s 1.82s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 139 ( 15 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 167 ( 67 ~; 43 |; 41 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 46 ( 1 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t14_yellow19,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
=> set_difference(X2,singleton(empty_set)) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_yellow19) ).
fof(t15_yellow19,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
=> X2 = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow19) ).
fof(t2_yellow19,axiom,
! [X1] :
( ~ empty(X1)
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(X1))
& upper_relstr_subset(X2,boole_POSet(X1))
& proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
& element(X2,powerset(the_carrier(boole_POSet(X1)))) )
=> ! [X3] :
~ ( in(X3,X2)
& empty(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_yellow19) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(t65_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(fc2_pre_topc,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(c_0_7,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
=> set_difference(X2,singleton(empty_set)) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
inference(fof_simplification,[status(thm)],[t14_yellow19]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
& proper_element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) )
=> X2 = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t15_yellow19])]) ).
fof(c_0_9,plain,
! [X1] :
( ~ empty(X1)
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,boole_POSet(X1))
& upper_relstr_subset(X2,boole_POSet(X1))
& proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
& element(X2,powerset(the_carrier(boole_POSet(X1)))) )
=> ! [X3] :
~ ( in(X3,X2)
& empty(X3) ) ) ),
inference(fof_simplification,[status(thm)],[t2_yellow19]) ).
fof(c_0_10,plain,
! [X384,X385] :
( empty_carrier(X384)
| ~ one_sorted_str(X384)
| empty(X385)
| ~ filtered_subset(X385,boole_POSet(cast_as_carrier_subset(X384)))
| ~ upper_relstr_subset(X385,boole_POSet(cast_as_carrier_subset(X384)))
| ~ element(X385,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X384)))))
| set_difference(X385,singleton(empty_set)) = filter_of_net_str(X384,net_of_bool_filter(X384,cast_as_carrier_subset(X384),X385)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_11,negated_conjecture,
( ~ empty_carrier(esk38_0)
& one_sorted_str(esk38_0)
& ~ empty(esk39_0)
& filtered_subset(esk39_0,boole_POSet(cast_as_carrier_subset(esk38_0)))
& upper_relstr_subset(esk39_0,boole_POSet(cast_as_carrier_subset(esk38_0)))
& proper_element(esk39_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk38_0)))))
& element(esk39_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk38_0)))))
& esk39_0 != filter_of_net_str(esk38_0,net_of_bool_filter(esk38_0,cast_as_carrier_subset(esk38_0),esk39_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X395,X396,X397] :
( empty(X395)
| empty(X396)
| ~ filtered_subset(X396,boole_POSet(X395))
| ~ upper_relstr_subset(X396,boole_POSet(X395))
| ~ proper_element(X396,powerset(the_carrier(boole_POSet(X395))))
| ~ element(X396,powerset(the_carrier(boole_POSet(X395))))
| ~ in(X397,X396)
| ~ empty(X397) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_13,plain,
! [X411,X412] :
( ~ in(X411,X412)
| ~ empty(X412) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_14,plain,
( empty_carrier(X1)
| empty(X2)
| set_difference(X2,singleton(empty_set)) = filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X2))
| ~ one_sorted_str(X1)
| ~ filtered_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
| ~ upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X1)))
| ~ element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1))))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
element(esk39_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk38_0))))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
upper_relstr_subset(esk39_0,boole_POSet(cast_as_carrier_subset(esk38_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
filtered_subset(esk39_0,boole_POSet(cast_as_carrier_subset(esk38_0))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
one_sorted_str(esk38_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
~ empty(esk39_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
~ empty_carrier(esk38_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_21,plain,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[t65_zfmisc_1]) ).
cnf(c_0_22,plain,
( empty(X1)
| empty(X2)
| ~ filtered_subset(X2,boole_POSet(X1))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ in(X3,X2)
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,negated_conjecture,
esk39_0 != filter_of_net_str(esk38_0,net_of_bool_filter(esk38_0,cast_as_carrier_subset(esk38_0),esk39_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,negated_conjecture,
filter_of_net_str(esk38_0,net_of_bool_filter(esk38_0,cast_as_carrier_subset(esk38_0),esk39_0)) = set_difference(esk39_0,singleton(empty_set)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]),c_0_18])]),c_0_19]),c_0_20]) ).
fof(c_0_26,plain,
! [X408,X409] :
( ( set_difference(X408,singleton(X409)) != X408
| ~ in(X409,X408) )
& ( in(X409,X408)
| set_difference(X408,singleton(X409)) = X408 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])]) ).
fof(c_0_27,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(cast_as_carrier_subset(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_pre_topc]) ).
cnf(c_0_28,plain,
( empty(X1)
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ empty(X3)
| ~ in(X3,X2) ),
inference(csr,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
proper_element(esk39_0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(esk38_0))))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
set_difference(esk39_0,singleton(empty_set)) != esk39_0,
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( in(X1,X2)
| set_difference(X2,singleton(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X287] :
( empty_carrier(X287)
| ~ one_sorted_str(X287)
| ~ empty(cast_as_carrier_subset(X287)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])]) ).
cnf(c_0_33,negated_conjecture,
( empty(cast_as_carrier_subset(esk38_0))
| ~ empty(X1)
| ~ in(X1,esk39_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_16]),c_0_17]),c_0_15])]) ).
cnf(c_0_34,negated_conjecture,
in(empty_set,esk39_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_36,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(cast_as_carrier_subset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
empty(cast_as_carrier_subset(esk38_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_18])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU394+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n004.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 03:03:32 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.48/1.82 % Version : CSE_E---1.7
% 1.48/1.82 % Problem : theBenchmark.p
% 1.48/1.82 % SZS status Theorem for theBenchmark.p
% 1.48/1.82 % SZS output start CNFRefutation
% See solution above
% 1.48/1.82 % Total time : 1.423s
%------------------------------------------------------------------------------