%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU326+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 : n018.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 08:45:49 AM UTC 2026
% Result : Theorem 0.15s 0.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 65 ( 49 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 68 ( 31 ~; 17 |; 15 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('theBenchmark.p',dt_k7_setfam_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(t46_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('theBenchmark.p',t46_setfam_1) ).
fof(t10_tops_2,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ~ ( B = empty_set
& complements_of_subsets(A,B) != empty_set )
& ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ) ),
file('theBenchmark.p',t10_tops_2) ).
fof(t10_tops_2_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ~ ( B = empty_set
& complements_of_subsets(A,B) != empty_set )
& ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ) ),
inference(assume_negation,[status(cth)],[t10_tops_2]) ).
cnf(c_68,plain,
( element(complements_of_subsets(B,A),powerset(powerset(B)))
| ~ element(A,powerset(powerset(B))) ),
inference(clausify,[status(thm)],[dt_k7_setfam_1]) ).
cnf(c_77,plain,
( complements_of_subsets(B,complements_of_subsets(B,A)) = A
| ~ element(A,powerset(powerset(B))) ),
inference(clausify,[status(thm)],[involutiveness_k7_setfam_1]) ).
cnf(c_90,plain,
( complements_of_subsets(B,A) != empty_set
| empty_set = A
| ~ element(A,powerset(powerset(B))) ),
inference(clausify,[status(thm)],[t46_setfam_1]) ).
fof(nnf_38,plain,
? [A,B] :
( ( ( empty_set = B
& complements_of_subsets(A,B) != empty_set )
| ( complements_of_subsets(A,B) = empty_set
& empty_set != B ) )
& element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t10_tops_2_neg]) ).
fof(sk_t10_tops_2_neg_sk,plain,
( ( ( empty_set = sK0
& complements_of_subsets(sK1,sK0) != empty_set )
| ( complements_of_subsets(sK1,sK0) = empty_set
& empty_set != sK0 ) )
& element(sK0,powerset(powerset(sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_38]) ).
fof(sk_t10_tops_2_neg,plain,
( ( empty_set = sK0
| complements_of_subsets(sK1,sK0) = empty_set )
& ( complements_of_subsets(sK1,sK0) != empty_set
| empty_set != sK0 )
& element(sK0,powerset(powerset(sK1))) ),
inference(cnf_transformation,[status(thm)],[sk_t10_tops_2_neg_sk]) ).
cnf(c_96,negated_conjecture,
element(sK0,powerset(powerset(sK1))),
inference(split_conjunct,[status(thm)],[sk_t10_tops_2_neg]) ).
cnf(c_97,negated_conjecture,
( complements_of_subsets(sK1,sK0) != empty_set
| empty_set != sK0 ),
inference(split_conjunct,[status(thm)],[sk_t10_tops_2_neg]) ).
cnf(c_98,negated_conjecture,
( complements_of_subsets(sK1,sK0) != empty_set
| sK0 != empty_set ),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_99,negated_conjecture,
( empty_set = sK0
| complements_of_subsets(sK1,sK0) = empty_set ),
inference(split_conjunct,[status(thm)],[sk_t10_tops_2_neg]) ).
cnf(c_100,negated_conjecture,
( sK0 = empty_set
| complements_of_subsets(sK1,sK0) = empty_set ),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_390,negated_conjecture,
( complements_of_subsets(sK1,sK0) != empty_set
| empty_set = sK0 ),
inference(resolve,[status(thm)],[c_96,c_90]) ).
cnf(c_184,negated_conjecture,
( complements_of_subsets(sK1,sK0) != empty_set
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_390]) ).
cnf(c_186,plain,
complements_of_subsets(sK1,complements_of_subsets(sK1,sK0)) = sK0,
inference(resolve,[status(thm)],[c_96,c_77]) ).
cnf(c_187,plain,
element(complements_of_subsets(sK1,sK0),powerset(powerset(sK1))),
inference(resolve,[status(thm)],[c_96,c_68]) ).
cnf(c_391,negated_conjecture,
( sK0 = empty_set
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_184,c_100]) ).
cnf(c_381,negated_conjecture,
sK0 = empty_set,
inference(copy,[status(thm)],[c_391]) ).
cnf(c_382,negated_conjecture,
complements_of_subsets(sK1,sK0) != empty_set,
inference(resolve,[status(thm)],[c_381,c_98]) ).
cnf(c_388,plain,
complements_of_subsets(sK1,complements_of_subsets(sK1,sK0)) = empty_set,
inference(paramod,[status(thm)],[c_381,c_186]) ).
cnf(c_392,plain,
( complements_of_subsets(sK1,complements_of_subsets(sK1,sK0)) != empty_set
| empty_set = complements_of_subsets(sK1,sK0) ),
inference(resolve,[status(thm)],[c_187,c_90]) ).
cnf(c_393,plain,
( complements_of_subsets(sK1,complements_of_subsets(sK1,sK0)) != empty_set
| complements_of_subsets(sK1,sK0) = empty_set ),
inference(copy,[status(thm)],[c_392]) ).
cnf(c_394,negated_conjecture,
complements_of_subsets(sK1,complements_of_subsets(sK1,sK0)) != empty_set,
inference(resolve,[status(thm)],[c_382,c_393]) ).
cnf(c_389,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_388,c_394]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU326+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n018.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 09:14:51 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 73085 was started by sandbox2 on n018,
% 0.15/0.43 % Sat Sep 26 09:14:51 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 0.15/0.51
% 0.15/0.51 % SZS status Theorem for theBenchmark
% 0.15/0.51
% 0.15/0.51 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.15/0.51 % Length of proof is 19.
% 0.15/0.51 % Level of proof is 5.
% 0.15/0.51 % Maximum clause weight is 31.000.
% 0.15/0.51 % Given clauses 191.
% 0.15/0.51
% 0.15/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------