%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU387+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 : n001.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 08:46:09 AM UTC 2026
% Result : Theorem 0.17s 5.91s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 20 unt; 0 def)
% Number of atoms : 176 ( 6 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 231 ( 96 ~; 77 |; 50 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 2 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 ( 7 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k3_yellow_1,axiom,
! [A] :
( rel_str(boole_POSet(A))
& strict_rel_str(boole_POSet(A)) ),
file('theBenchmark.p',dt_k3_yellow_1) ).
fof(fc1_waybel_7,axiom,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& boolean_relstr(boole_POSet(A))
& complemented_relstr(boole_POSet(A))
& heyting_relstr(boole_POSet(A))
& distributive_relstr(boole_POSet(A))
& ~ v1_yellow_3(boole_POSet(A))
& join_complete_relstr(boole_POSet(A))
& up_complete_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
file('theBenchmark.p',fc1_waybel_7) ).
fof(t18_yellow_1,axiom,
! [A] : bottom_of_relstr(boole_POSet(A)) = empty_set,
file('theBenchmark.p',t18_yellow_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t8_waybel_7,axiom,
! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( element(B,powerset(the_carrier(A)))
& upper_relstr_subset(B,A)
& filtered_subset(B,A)
& ~ empty(B) )
=> ( proper_element(B,powerset(the_carrier(A)))
<=> ~ in(bottom_of_relstr(A),B) ) ) ),
file('theBenchmark.p',t8_waybel_7) ).
fof(t2_yellow19,conjecture,
! [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(t2_yellow19_neg,negated_conjecture,
~ ! [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) ) ) ),
inference(assume_negation,[status(cth)],[t2_yellow19]) ).
cnf(c_112,plain,
rel_str(boole_POSet(A)),
inference(clausify,[status(thm)],[dt_k3_yellow_1]) ).
cnf(c_133,plain,
( ~ in(bottom_of_relstr(A),B)
| ~ proper_element(B,powerset(the_carrier(A)))
| ~ element(B,powerset(the_carrier(A)))
| ~ upper_relstr_subset(B,A)
| ~ filtered_subset(B,A)
| empty(B)
| ~ rel_str(A)
| ~ lower_bounded_relstr(A)
| ~ antisymmetric_relstr(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[t8_waybel_7]) ).
cnf(c_261,plain,
~ empty_carrier(boole_POSet(A)),
inference(clausify,[status(thm)],[fc1_waybel_7]) ).
cnf(c_262,plain,
reflexive_relstr(boole_POSet(A)),
inference(clausify,[status(thm)],[fc1_waybel_7]) ).
cnf(c_263,plain,
transitive_relstr(boole_POSet(A)),
inference(clausify,[status(thm)],[fc1_waybel_7]) ).
cnf(c_264,plain,
antisymmetric_relstr(boole_POSet(A)),
inference(clausify,[status(thm)],[fc1_waybel_7]) ).
cnf(c_265,plain,
lower_bounded_relstr(boole_POSet(A)),
inference(clausify,[status(thm)],[fc1_waybel_7]) ).
cnf(c_361,plain,
bottom_of_relstr(boole_POSet(A)) = empty_set,
inference(clausify,[status(thm)],[t18_yellow_1]) ).
cnf(c_366,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
fof(nnf_85,plain,
? [A] :
( ? [B] :
( ? [C] :
( 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(fof_nnf,[status(thm)],[t2_yellow19_neg]) ).
fof(sk_t2_yellow19_neg,plain,
( empty(sK2)
& in(sK2,sK0)
& element(sK0,powerset(the_carrier(boole_POSet(sK1))))
& proper_element(sK0,powerset(the_carrier(boole_POSet(sK1))))
& upper_relstr_subset(sK0,boole_POSet(sK1))
& filtered_subset(sK0,boole_POSet(sK1))
& ~ empty(sK0)
& ~ empty(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2]),skolemize(A,sK1),skolemize(B,sK0),skolemize(C,sK2)],[nnf_85]) ).
cnf(c_370,negated_conjecture,
~ empty(sK0),
inference(split_conjunct,[status(thm)],[sk_t2_yellow19_neg]) ).
cnf(c_371,negated_conjecture,
filtered_subset(sK0,boole_POSet(sK1)),
inference(split_conjunct,[status(thm)],[sk_t2_yellow19_neg]) ).
cnf(c_372,negated_conjecture,
upper_relstr_subset(sK0,boole_POSet(sK1)),
inference(split_conjunct,[status(thm)],[sk_t2_yellow19_neg]) ).
cnf(c_373,negated_conjecture,
proper_element(sK0,powerset(the_carrier(boole_POSet(sK1)))),
inference(split_conjunct,[status(thm)],[sk_t2_yellow19_neg]) ).
cnf(c_374,negated_conjecture,
element(sK0,powerset(the_carrier(boole_POSet(sK1)))),
inference(split_conjunct,[status(thm)],[sk_t2_yellow19_neg]) ).
cnf(c_375,negated_conjecture,
in(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_t2_yellow19_neg]) ).
cnf(c_376,negated_conjecture,
empty(sK2),
inference(split_conjunct,[status(thm)],[sk_t2_yellow19_neg]) ).
cnf(c_759,plain,
( ~ in(bottom_of_relstr(boole_POSet(A)),B)
| ~ proper_element(B,powerset(the_carrier(boole_POSet(A))))
| ~ element(B,powerset(the_carrier(boole_POSet(A))))
| ~ upper_relstr_subset(B,boole_POSet(A))
| ~ filtered_subset(B,boole_POSet(A))
| empty(B)
| ~ lower_bounded_relstr(boole_POSet(A))
| ~ antisymmetric_relstr(boole_POSet(A))
| ~ transitive_relstr(boole_POSet(A))
| ~ reflexive_relstr(boole_POSet(A))
| empty_carrier(boole_POSet(A)) ),
inference(resolve,[status(thm)],[c_133,c_112]) ).
cnf(c_1117,plain,
( ~ in(empty_set,B)
| ~ proper_element(B,powerset(the_carrier(boole_POSet(A))))
| ~ element(B,powerset(the_carrier(boole_POSet(A))))
| ~ upper_relstr_subset(B,boole_POSet(A))
| ~ filtered_subset(B,boole_POSet(A))
| empty(B)
| ~ lower_bounded_relstr(boole_POSet(A))
| ~ antisymmetric_relstr(boole_POSet(A))
| ~ transitive_relstr(boole_POSet(A))
| ~ reflexive_relstr(boole_POSet(A))
| empty_carrier(boole_POSet(A)) ),
inference(paramod,[status(thm)],[c_361,c_759]) ).
cnf(c_1118,plain,
( ~ in(empty_set,B)
| ~ proper_element(B,powerset(the_carrier(boole_POSet(A))))
| ~ element(B,powerset(the_carrier(boole_POSet(A))))
| ~ upper_relstr_subset(B,boole_POSet(A))
| ~ filtered_subset(B,boole_POSet(A))
| empty(B)
| ~ lower_bounded_relstr(boole_POSet(A))
| ~ antisymmetric_relstr(boole_POSet(A))
| ~ transitive_relstr(boole_POSet(A))
| ~ reflexive_relstr(boole_POSet(A)) ),
inference(resolve,[status(thm)],[c_261,c_1117]) ).
cnf(c_1119,plain,
( ~ in(empty_set,B)
| ~ proper_element(B,powerset(the_carrier(boole_POSet(A))))
| ~ element(B,powerset(the_carrier(boole_POSet(A))))
| ~ upper_relstr_subset(B,boole_POSet(A))
| ~ filtered_subset(B,boole_POSet(A))
| empty(B)
| ~ lower_bounded_relstr(boole_POSet(A))
| ~ antisymmetric_relstr(boole_POSet(A))
| ~ transitive_relstr(boole_POSet(A)) ),
inference(resolve,[status(thm)],[c_262,c_1118]) ).
cnf(c_1120,plain,
( ~ in(empty_set,B)
| ~ proper_element(B,powerset(the_carrier(boole_POSet(A))))
| ~ element(B,powerset(the_carrier(boole_POSet(A))))
| ~ upper_relstr_subset(B,boole_POSet(A))
| ~ filtered_subset(B,boole_POSet(A))
| empty(B)
| ~ lower_bounded_relstr(boole_POSet(A))
| ~ antisymmetric_relstr(boole_POSet(A)) ),
inference(resolve,[status(thm)],[c_263,c_1119]) ).
cnf(c_1121,plain,
( ~ in(empty_set,B)
| ~ proper_element(B,powerset(the_carrier(boole_POSet(A))))
| ~ element(B,powerset(the_carrier(boole_POSet(A))))
| ~ upper_relstr_subset(B,boole_POSet(A))
| ~ filtered_subset(B,boole_POSet(A))
| empty(B)
| ~ lower_bounded_relstr(boole_POSet(A)) ),
inference(resolve,[status(thm)],[c_264,c_1120]) ).
cnf(c_760,plain,
( ~ in(empty_set,A)
| ~ proper_element(A,powerset(the_carrier(boole_POSet(B))))
| ~ element(A,powerset(the_carrier(boole_POSet(B))))
| ~ upper_relstr_subset(A,boole_POSet(B))
| ~ filtered_subset(A,boole_POSet(B))
| empty(A) ),
inference(resolve,[status(thm)],[c_265,c_1121]) ).
cnf(c_1122,negated_conjecture,
empty_set = sK2,
inference(resolve,[status(thm)],[c_376,c_366]) ).
cnf(c_989,negated_conjecture,
sK2 = empty_set,
inference(copy,[status(thm)],[c_1122]) ).
cnf(c_992,negated_conjecture,
in(empty_set,sK0),
inference(paramod,[status(thm)],[c_989,c_375]) ).
cnf(c_1123,negated_conjecture,
( ~ in(empty_set,sK0)
| ~ proper_element(sK0,powerset(the_carrier(boole_POSet(sK1))))
| ~ element(sK0,powerset(the_carrier(boole_POSet(sK1))))
| ~ upper_relstr_subset(sK0,boole_POSet(sK1))
| empty(sK0) ),
inference(resolve,[status(thm)],[c_760,c_371]) ).
cnf(c_1124,negated_conjecture,
( ~ in(empty_set,sK0)
| ~ proper_element(sK0,powerset(the_carrier(boole_POSet(sK1))))
| ~ element(sK0,powerset(the_carrier(boole_POSet(sK1))))
| ~ upper_relstr_subset(sK0,boole_POSet(sK1)) ),
inference(resolve,[status(thm)],[c_370,c_1123]) ).
cnf(c_1125,negated_conjecture,
( ~ in(empty_set,sK0)
| ~ proper_element(sK0,powerset(the_carrier(boole_POSet(sK1))))
| ~ element(sK0,powerset(the_carrier(boole_POSet(sK1)))) ),
inference(resolve,[status(thm)],[c_372,c_1124]) ).
cnf(c_1126,negated_conjecture,
( ~ in(empty_set,sK0)
| ~ proper_element(sK0,powerset(the_carrier(boole_POSet(sK1)))) ),
inference(resolve,[status(thm)],[c_374,c_1125]) ).
cnf(c_1127,negated_conjecture,
~ in(empty_set,sK0),
inference(resolve,[status(thm)],[c_373,c_1126]) ).
cnf(c_1116,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_992,c_1127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU387+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.39 % Computer : n001.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.39 % CPULimit : 300
% 0.13/5.39 % WCLimit : 300
% 0.13/5.39 % DateTime : Sat Sep 26 09:29:50 UTC 2026
% 0.13/5.39 % CPUTime :
% 0.13/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.40 % Process 1491634 was started by sandbox2 on n001,
% 0.13/5.40 % Sat Sep 26 09:29:50 2026
% 0.13/5.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.43
% 0.17/5.43 % From the command line: assign(max_seconds, 300).
% 0.17/5.91
% 0.17/5.91 % SZS status Theorem for theBenchmark
% 0.17/5.91
% 0.17/5.91 % Proof 1 at 0.42 (+ 0.03) seconds.
% 0.17/5.91 % Length of proof is 27.
% 0.17/5.91 % Level of proof is 4.
% 0.17/5.91 % Maximum clause weight is 45.000.
% 0.17/5.91 % Given clauses 377.
% 0.17/5.91
% 0.17/5.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------