%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU319+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 08:45:47 AM UTC 2026
% Result : Theorem 0.14s 5.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 74 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 27 ~; 26 |; 6 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 22 ( 0 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d6_pre_topc,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A) ) ) ),
file('theBenchmark.p',d6_pre_topc) ).
fof(dt_l1_pre_topc,axiom,
! [A] :
( top_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_pre_topc) ).
fof(t17_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
file('theBenchmark.p',t17_pre_topc) ).
fof(t29_tops_1,conjecture,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('theBenchmark.p',t29_tops_1) ).
fof(t29_tops_1_neg,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(assume_negation,[status(cth)],[t29_tops_1]) ).
cnf(c_21,plain,
( one_sorted_str(A)
| ~ top_str(A) ),
inference(clausify,[status(thm)],[dt_l1_pre_topc]) ).
cnf(c_22,plain,
( ~ open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A)
| closed_subset(B,A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(clausify,[status(thm)],[d6_pre_topc]) ).
cnf(c_23,plain,
( open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A)
| ~ closed_subset(B,A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(clausify,[status(thm)],[d6_pre_topc]) ).
fof(nnf_19,plain,
? [A] :
( ? [B] :
( ( ~ open_subset(subset_complement(the_carrier(A),B),A)
| ~ closed_subset(B,A) )
& ( open_subset(subset_complement(the_carrier(A),B),A)
| closed_subset(B,A) )
& element(B,powerset(the_carrier(A))) )
& top_str(A) ),
inference(fof_nnf,[status(thm)],[t29_tops_1_neg]) ).
fof(sk_t29_tops_1_neg,plain,
( ( ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0) )
& ( open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| closed_subset(sK1,sK0) )
& element(sK1,powerset(the_carrier(sK0)))
& top_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_19]) ).
cnf(c_24,negated_conjecture,
top_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t29_tops_1_neg]) ).
cnf(c_25,plain,
( subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)
| ~ element(B,powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[t17_pre_topc]) ).
cnf(c_27,negated_conjecture,
one_sorted_str(sK0),
inference(resolve,[status(thm)],[c_24,c_21]) ).
cnf(c_34,negated_conjecture,
( open_subset(subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),A),sK0)
| ~ closed_subset(A,sK0)
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_35,negated_conjecture,
( ~ open_subset(subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),A),sK0)
| closed_subset(A,sK0)
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_38,negated_conjecture,
( ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0) ),
inference(split_conjunct,[status(thm)],[sk_t29_tops_1_neg]) ).
cnf(c_39,negated_conjecture,
( open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| closed_subset(sK1,sK0) ),
inference(split_conjunct,[status(thm)],[sk_t29_tops_1_neg]) ).
cnf(c_40,negated_conjecture,
element(sK1,powerset(the_carrier(sK0))),
inference(split_conjunct,[status(thm)],[sk_t29_tops_1_neg]) ).
cnf(c_49,negated_conjecture,
( subset_complement(the_carrier(sK0),A) = subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),A)
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_25,c_27]) ).
cnf(c_50,negated_conjecture,
( subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),A) = subset_complement(the_carrier(sK0),A)
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_62,plain,
( ~ open_subset(subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1),sK0)
| closed_subset(sK1,sK0) ),
inference(resolve,[status(thm)],[c_40,c_35]) ).
cnf(c_63,plain,
( open_subset(subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0) ),
inference(resolve,[status(thm)],[c_40,c_34]) ).
cnf(c_93,plain,
subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK1) = subset_complement(the_carrier(sK0),sK1),
inference(resolve,[status(thm)],[c_50,c_40]) ).
cnf(c_97,plain,
( open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ closed_subset(sK1,sK0) ),
inference(paramod,[status(thm)],[c_93,c_63]) ).
cnf(c_98,plain,
( ~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| closed_subset(sK1,sK0) ),
inference(paramod,[status(thm)],[c_93,c_62]) ).
cnf(c_392,negated_conjecture,
( closed_subset(sK1,sK0)
| closed_subset(sK1,sK0) ),
inference(resolve,[status(thm)],[c_98,c_39]) ).
cnf(c_389,negated_conjecture,
closed_subset(sK1,sK0),
inference(copy,[status(thm)],[c_392]) ).
cnf(c_390,plain,
open_subset(subset_complement(the_carrier(sK0),sK1),sK0),
inference(resolve,[status(thm)],[c_389,c_97]) ).
cnf(c_393,negated_conjecture,
~ open_subset(subset_complement(the_carrier(sK0),sK1),sK0),
inference(resolve,[status(thm)],[c_389,c_38]) ).
cnf(c_391,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_390,c_393]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU319+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n015.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 09:14:35 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 3673258 was started by sandbox on n015,
% 0.11/5.38 % Sat Sep 26 09:14:35 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.14/5.43
% 0.14/5.43 % SZS status Theorem for theBenchmark
% 0.14/5.43
% 0.14/5.43 % Proof 1 at 0.02 (+ 0.02) seconds.
% 0.14/5.43 % Length of proof is 25.
% 0.14/5.43 % Level of proof is 9.
% 0.14/5.43 % Maximum clause weight is 31.000.
% 0.14/5.43 % Given clauses 45.
% 0.14/5.43
% 0.14/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------