%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU320+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 : n003.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 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 69 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 66 ( 25 ~; 24 |; 6 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k3_subset_1) ).
fof(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('theBenchmark.p',involutiveness_k3_subset_1) ).
fof(t29_tops_1,axiom,
! [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(t30_tops_1,conjecture,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('theBenchmark.p',t30_tops_1) ).
fof(t30_tops_1_neg,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(assume_negation,[status(cth)],[t30_tops_1]) ).
cnf(c_17,plain,
( open_subset(subset_complement(the_carrier(A),B),A)
| ~ closed_subset(B,A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(clausify,[status(thm)],[t29_tops_1]) ).
cnf(c_18,plain,
( ~ open_subset(subset_complement(the_carrier(A),B),A)
| closed_subset(B,A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(clausify,[status(thm)],[t29_tops_1]) ).
fof(nnf_14,plain,
? [A] :
( ? [B] :
( ( ~ closed_subset(subset_complement(the_carrier(A),B),A)
| ~ open_subset(B,A) )
& ( closed_subset(subset_complement(the_carrier(A),B),A)
| open_subset(B,A) )
& element(B,powerset(the_carrier(A))) )
& top_str(A) ),
inference(fof_nnf,[status(thm)],[t30_tops_1_neg]) ).
fof(sk_t30_tops_1_neg,plain,
( ( ~ closed_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ open_subset(sK1,sK0) )
& ( closed_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| open_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_14]) ).
cnf(c_19,negated_conjecture,
top_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t30_tops_1_neg]) ).
cnf(c_24,negated_conjecture,
( open_subset(subset_complement(the_carrier(sK0),A),sK0)
| ~ closed_subset(A,sK0)
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_19,c_17]) ).
cnf(c_25,negated_conjecture,
( ~ open_subset(subset_complement(the_carrier(sK0),A),sK0)
| closed_subset(A,sK0)
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_19,c_18]) ).
cnf(c_28,negated_conjecture,
( ~ closed_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ open_subset(sK1,sK0) ),
inference(split_conjunct,[status(thm)],[sk_t30_tops_1_neg]) ).
cnf(c_29,negated_conjecture,
( closed_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| open_subset(sK1,sK0) ),
inference(split_conjunct,[status(thm)],[sk_t30_tops_1_neg]) ).
cnf(c_30,negated_conjecture,
element(sK1,powerset(the_carrier(sK0))),
inference(split_conjunct,[status(thm)],[sk_t30_tops_1_neg]) ).
cnf(c_31,plain,
( subset_complement(B,subset_complement(B,A)) = A
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[involutiveness_k3_subset_1]) ).
cnf(c_33,plain,
( element(subset_complement(B,A),powerset(B))
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[dt_k3_subset_1]) ).
cnf(c_34,plain,
subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK1)) = sK1,
inference(resolve,[status(thm)],[c_31,c_30]) ).
cnf(c_38,plain,
element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0))),
inference(resolve,[status(thm)],[c_33,c_30]) ).
cnf(c_48,plain,
( ~ open_subset(sK1,sK0)
| closed_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| ~ element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0))) ),
inference(paramod,[status(thm)],[c_34,c_25]) ).
cnf(c_40,plain,
( ~ open_subset(sK1,sK0)
| closed_subset(subset_complement(the_carrier(sK0),sK1),sK0) ),
inference(resolve,[status(thm)],[c_38,c_48]) ).
cnf(c_49,negated_conjecture,
( closed_subset(subset_complement(the_carrier(sK0),sK1),sK0)
| closed_subset(subset_complement(the_carrier(sK0),sK1),sK0) ),
inference(resolve,[status(thm)],[c_40,c_29]) ).
cnf(c_45,negated_conjecture,
closed_subset(subset_complement(the_carrier(sK0),sK1),sK0),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_46,negated_conjecture,
~ open_subset(sK1,sK0),
inference(resolve,[status(thm)],[c_45,c_28]) ).
cnf(c_50,negated_conjecture,
( open_subset(subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK1)),sK0)
| ~ element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_45,c_24]) ).
cnf(c_51,negated_conjecture,
( open_subset(sK1,sK0)
| ~ element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0))) ),
inference(paramod,[status(thm)],[c_34,c_50]) ).
cnf(c_52,negated_conjecture,
open_subset(sK1,sK0),
inference(resolve,[status(thm)],[c_38,c_51]) ).
cnf(c_47,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_46,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU320+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 09:13:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 2530564 was started by sandbox2 on n003,
% 0.11/0.38 % Sat Sep 26 09:13:39 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 0.11/0.40
% 0.11/0.40 % SZS status Theorem for theBenchmark
% 0.11/0.40
% 0.11/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.40 % Length of proof is 20.
% 0.11/0.40 % Level of proof is 6.
% 0.11/0.40 % Maximum clause weight is 14.000.
% 0.11/0.40 % Given clauses 19.
% 0.11/0.40
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------