%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU387+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 : n006.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 05:12:08 PM UTC 2026
% Result : Theorem 1.30s 1.74s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 18 unt; 0 def)
% Number of atoms : 183 ( 7 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 213 ( 67 ~; 47 |; 88 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-1 aty)
% Number of variables : 39 ( 8 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t2_yellow19,conjecture,
! [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(t8_waybel_7,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& transitive_relstr(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,X1)
& upper_relstr_subset(X2,X1)
& element(X2,powerset(the_carrier(X1))) )
=> ( proper_element(X2,powerset(the_carrier(X1)))
<=> ~ in(bottom_of_relstr(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel_7) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(fc1_waybel_7,axiom,
! [X1] :
( ~ empty_carrier(boole_POSet(X1))
& strict_rel_str(boole_POSet(X1))
& reflexive_relstr(boole_POSet(X1))
& transitive_relstr(boole_POSet(X1))
& antisymmetric_relstr(boole_POSet(X1))
& lower_bounded_relstr(boole_POSet(X1))
& upper_bounded_relstr(boole_POSet(X1))
& bounded_relstr(boole_POSet(X1))
& up_complete_relstr(boole_POSet(X1))
& join_complete_relstr(boole_POSet(X1))
& ~ v1_yellow_3(boole_POSet(X1))
& distributive_relstr(boole_POSet(X1))
& heyting_relstr(boole_POSet(X1))
& complemented_relstr(boole_POSet(X1))
& boolean_relstr(boole_POSet(X1))
& with_suprema_relstr(boole_POSet(X1))
& with_infima_relstr(boole_POSet(X1))
& complete_relstr(boole_POSet(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel_7) ).
fof(t18_yellow_1,axiom,
! [X1] : bottom_of_relstr(boole_POSet(X1)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_yellow_1) ).
fof(dt_k3_yellow_1,axiom,
! [X1] :
( strict_rel_str(boole_POSet(X1))
& rel_str(boole_POSet(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
fof(c_0_7,negated_conjecture,
~ ! [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)],[inference(assume_negation,[status(cth)],[t2_yellow19])]) ).
fof(c_0_8,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& reflexive_relstr(X1)
& transitive_relstr(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( ( ~ empty(X2)
& filtered_subset(X2,X1)
& upper_relstr_subset(X2,X1)
& element(X2,powerset(the_carrier(X1))) )
=> ( proper_element(X2,powerset(the_carrier(X1)))
<=> ~ in(bottom_of_relstr(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[t8_waybel_7]) ).
fof(c_0_9,plain,
! [X231] :
( ~ empty(X231)
| X231 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_10,negated_conjecture,
( ~ empty(esk28_0)
& ~ empty(esk29_0)
& filtered_subset(esk29_0,boole_POSet(esk28_0))
& upper_relstr_subset(esk29_0,boole_POSet(esk28_0))
& proper_element(esk29_0,powerset(the_carrier(boole_POSet(esk28_0))))
& element(esk29_0,powerset(the_carrier(boole_POSet(esk28_0))))
& in(esk30_0,esk29_0)
& empty(esk30_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_11,plain,
! [X236,X237] :
( ( ~ proper_element(X237,powerset(the_carrier(X236)))
| ~ in(bottom_of_relstr(X236),X237)
| empty(X237)
| ~ filtered_subset(X237,X236)
| ~ upper_relstr_subset(X237,X236)
| ~ element(X237,powerset(the_carrier(X236)))
| empty_carrier(X236)
| ~ reflexive_relstr(X236)
| ~ transitive_relstr(X236)
| ~ antisymmetric_relstr(X236)
| ~ lower_bounded_relstr(X236)
| ~ rel_str(X236) )
& ( in(bottom_of_relstr(X236),X237)
| proper_element(X237,powerset(the_carrier(X236)))
| empty(X237)
| ~ filtered_subset(X237,X236)
| ~ upper_relstr_subset(X237,X236)
| ~ element(X237,powerset(the_carrier(X236)))
| empty_carrier(X236)
| ~ reflexive_relstr(X236)
| ~ transitive_relstr(X236)
| ~ antisymmetric_relstr(X236)
| ~ lower_bounded_relstr(X236)
| ~ rel_str(X236) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_12,plain,
! [X232,X233] :
( ~ in(X232,X233)
| ~ empty(X233) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_13,plain,
! [X1] :
( ~ empty_carrier(boole_POSet(X1))
& strict_rel_str(boole_POSet(X1))
& reflexive_relstr(boole_POSet(X1))
& transitive_relstr(boole_POSet(X1))
& antisymmetric_relstr(boole_POSet(X1))
& lower_bounded_relstr(boole_POSet(X1))
& upper_bounded_relstr(boole_POSet(X1))
& bounded_relstr(boole_POSet(X1))
& up_complete_relstr(boole_POSet(X1))
& join_complete_relstr(boole_POSet(X1))
& ~ v1_yellow_3(boole_POSet(X1))
& distributive_relstr(boole_POSet(X1))
& heyting_relstr(boole_POSet(X1))
& complemented_relstr(boole_POSet(X1))
& boolean_relstr(boole_POSet(X1))
& with_suprema_relstr(boole_POSet(X1))
& with_infima_relstr(boole_POSet(X1))
& complete_relstr(boole_POSet(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_waybel_7]) ).
cnf(c_0_14,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
empty(esk30_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( empty(X1)
| empty_carrier(X2)
| ~ proper_element(X1,powerset(the_carrier(X2)))
| ~ in(bottom_of_relstr(X2),X1)
| ~ filtered_subset(X1,X2)
| ~ upper_relstr_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ reflexive_relstr(X2)
| ~ transitive_relstr(X2)
| ~ antisymmetric_relstr(X2)
| ~ lower_bounded_relstr(X2)
| ~ rel_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X169] :
( ~ empty_carrier(boole_POSet(X169))
& strict_rel_str(boole_POSet(X169))
& reflexive_relstr(boole_POSet(X169))
& transitive_relstr(boole_POSet(X169))
& antisymmetric_relstr(boole_POSet(X169))
& lower_bounded_relstr(boole_POSet(X169))
& upper_bounded_relstr(boole_POSet(X169))
& bounded_relstr(boole_POSet(X169))
& up_complete_relstr(boole_POSet(X169))
& join_complete_relstr(boole_POSet(X169))
& ~ v1_yellow_3(boole_POSet(X169))
& distributive_relstr(boole_POSet(X169))
& heyting_relstr(boole_POSet(X169))
& complemented_relstr(boole_POSet(X169))
& boolean_relstr(boole_POSet(X169))
& with_suprema_relstr(boole_POSet(X169))
& with_infima_relstr(boole_POSet(X169))
& complete_relstr(boole_POSet(X169)) ),
inference(variable_rename,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X215] : bottom_of_relstr(boole_POSet(X215)) = empty_set,
inference(variable_rename,[status(thm)],[t18_yellow_1]) ).
cnf(c_0_20,negated_conjecture,
in(esk30_0,esk29_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
esk30_0 = empty_set,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_22,plain,
! [X149] :
( strict_rel_str(boole_POSet(X149))
& rel_str(boole_POSet(X149)) ),
inference(variable_rename,[status(thm)],[dt_k3_yellow_1]) ).
cnf(c_0_23,plain,
( empty_carrier(X1)
| ~ proper_element(X2,powerset(the_carrier(X1)))
| ~ upper_relstr_subset(X2,X1)
| ~ filtered_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ antisymmetric_relstr(X1)
| ~ transitive_relstr(X1)
| ~ lower_bounded_relstr(X1)
| ~ reflexive_relstr(X1)
| ~ in(bottom_of_relstr(X1),X2)
| ~ rel_str(X1) ),
inference(csr,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
proper_element(esk29_0,powerset(the_carrier(boole_POSet(esk28_0)))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,negated_conjecture,
upper_relstr_subset(esk29_0,boole_POSet(esk28_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
filtered_subset(esk29_0,boole_POSet(esk28_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,negated_conjecture,
element(esk29_0,powerset(the_carrier(boole_POSet(esk28_0)))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,plain,
antisymmetric_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
transitive_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,plain,
lower_bounded_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,plain,
reflexive_relstr(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_32,plain,
bottom_of_relstr(boole_POSet(X1)) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_33,negated_conjecture,
in(empty_set,esk29_0),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_34,plain,
rel_str(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,plain,
~ empty_carrier(boole_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),c_0_34])]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU387+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.16/0.32 % Computer : n006.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 03:01:31 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.30/1.74 % Version : CSE_E---1.7
% 1.30/1.74 % Problem : theBenchmark.p
% 1.30/1.74 % SZS status Theorem for theBenchmark.p
% 1.30/1.74 % SZS output start CNFRefutation
% See solution above
% 1.30/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------