%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU328+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 : 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 08:45:49 AM UTC 2026
% Result : Theorem 0.86s 0.56s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 20 unt; 0 def)
% Number of atoms : 75 ( 42 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 25 ~; 16 |; 5 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 46 ( 1 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_subset_1,axiom,
! [A] : cast_to_subset(A) = A,
file('theBenchmark.p',d4_subset_1) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
fof(dt_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(meet_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k6_setfam_1) ).
fof(redefinition_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> meet_of_subsets(A,B) = set_meet(B) ),
file('theBenchmark.p',redefinition_k6_setfam_1) ).
fof(redefinition_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k6_subset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t48_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ) ),
file('theBenchmark.p',t48_setfam_1) ).
fof(t12_tops_2,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,meet_of_subsets(A,B)) ) ),
file('theBenchmark.p',t12_tops_2) ).
fof(t12_tops_2_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,meet_of_subsets(A,B)) ) ),
inference(assume_negation,[status(cth)],[t12_tops_2]) ).
cnf(c_61,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_62,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_63,plain,
element(A,powerset(A)),
inference(resolve,[status(thm)],[c_62,c_61]) ).
cnf(c_89,plain,
cast_to_subset(A) = A,
inference(clausify,[status(thm)],[d4_subset_1]) ).
cnf(c_90,plain,
( set_difference(B,A) = subset_complement(B,A)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[d5_subset_1]) ).
cnf(c_91,plain,
( subset_complement(B,A) = set_difference(B,A)
| ~ element(A,powerset(B)) ),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_95,plain,
( element(meet_of_subsets(B,A),powerset(B))
| ~ element(A,powerset(powerset(B))) ),
inference(clausify,[status(thm)],[dt_k6_setfam_1]) ).
cnf(c_135,plain,
( set_meet(A) = meet_of_subsets(B,A)
| ~ element(A,powerset(powerset(B))) ),
inference(clausify,[status(thm)],[redefinition_k6_setfam_1]) ).
cnf(c_136,plain,
( meet_of_subsets(B,A) = set_meet(A)
| ~ element(A,powerset(powerset(B))) ),
inference(copy,[status(thm)],[c_135]) ).
cnf(c_137,plain,
( subset_difference(B,A,C) = set_difference(A,C)
| ~ element(C,powerset(B))
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[redefinition_k6_subset_1]) ).
cnf(c_141,plain,
( subset_difference(B,cast_to_subset(B),meet_of_subsets(B,A)) = union_of_subsets(B,complements_of_subsets(B,A))
| empty_set = A
| ~ element(A,powerset(powerset(B))) ),
inference(clausify,[status(thm)],[t48_setfam_1]) ).
cnf(c_142,plain,
( subset_difference(B,B,meet_of_subsets(B,A)) = union_of_subsets(B,complements_of_subsets(B,A))
| empty_set = A
| ~ element(A,powerset(powerset(B))) ),
inference(paramod,[status(thm)],[c_89,c_141]) ).
fof(nnf_59,plain,
? [A,B] :
( union_of_subsets(A,complements_of_subsets(A,B)) != subset_complement(A,meet_of_subsets(A,B))
& empty_set != B
& element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t12_tops_2_neg]) ).
fof(sk_t12_tops_2_neg,plain,
( union_of_subsets(sK1,complements_of_subsets(sK1,sK0)) != subset_complement(sK1,meet_of_subsets(sK1,sK0))
& empty_set != sK0
& element(sK0,powerset(powerset(sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_59]) ).
cnf(c_149,negated_conjecture,
element(sK0,powerset(powerset(sK1))),
inference(split_conjunct,[status(thm)],[sk_t12_tops_2_neg]) ).
cnf(c_150,negated_conjecture,
empty_set != sK0,
inference(split_conjunct,[status(thm)],[sk_t12_tops_2_neg]) ).
cnf(c_151,negated_conjecture,
sK0 != empty_set,
inference(copy,[status(thm)],[c_150]) ).
cnf(c_152,negated_conjecture,
union_of_subsets(sK1,complements_of_subsets(sK1,sK0)) != subset_complement(sK1,meet_of_subsets(sK1,sK0)),
inference(split_conjunct,[status(thm)],[sk_t12_tops_2_neg]) ).
cnf(c_392,plain,
meet_of_subsets(sK1,sK0) = set_meet(sK0),
inference(resolve,[status(thm)],[c_149,c_136]) ).
cnf(c_838,negated_conjecture,
element(meet_of_subsets(sK1,sK0),powerset(sK1)),
inference(resolve,[status(thm)],[c_149,c_95]) ).
cnf(c_399,negated_conjecture,
element(set_meet(sK0),powerset(sK1)),
inference(paramod,[status(thm)],[c_392,c_838]) ).
cnf(c_839,negated_conjecture,
( subset_difference(sK1,sK1,meet_of_subsets(sK1,sK0)) = union_of_subsets(sK1,complements_of_subsets(sK1,sK0))
| empty_set = sK0 ),
inference(resolve,[status(thm)],[c_142,c_149]) ).
cnf(c_840,negated_conjecture,
( subset_difference(sK1,sK1,set_meet(sK0)) = union_of_subsets(sK1,complements_of_subsets(sK1,sK0))
| empty_set = sK0 ),
inference(paramod,[status(thm)],[c_392,c_839]) ).
cnf(c_841,negated_conjecture,
( subset_difference(sK1,sK1,set_meet(sK0)) = union_of_subsets(sK1,complements_of_subsets(sK1,sK0))
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_840]) ).
cnf(c_418,negated_conjecture,
subset_difference(sK1,sK1,set_meet(sK0)) = union_of_subsets(sK1,complements_of_subsets(sK1,sK0)),
inference(resolve,[status(thm)],[c_151,c_841]) ).
cnf(c_433,negated_conjecture,
union_of_subsets(sK1,complements_of_subsets(sK1,sK0)) != subset_complement(sK1,set_meet(sK0)),
inference(paramod,[status(thm)],[c_392,c_152]) ).
cnf(c_797,plain,
subset_complement(sK1,set_meet(sK0)) = set_difference(sK1,set_meet(sK0)),
inference(resolve,[status(thm)],[c_399,c_91]) ).
cnf(c_842,plain,
( subset_difference(B,B,A) = set_difference(B,A)
| ~ element(A,powerset(B)) ),
inference(resolve,[status(thm)],[c_137,c_63]) ).
cnf(c_843,plain,
subset_difference(sK1,sK1,set_meet(sK0)) = set_difference(sK1,set_meet(sK0)),
inference(resolve,[status(thm)],[c_842,c_399]) ).
cnf(c_819,plain,
union_of_subsets(sK1,complements_of_subsets(sK1,sK0)) = set_difference(sK1,set_meet(sK0)),
inference(paramod,[status(thm)],[c_418,c_843]) ).
cnf(c_844,negated_conjecture,
set_difference(sK1,set_meet(sK0)) != subset_complement(sK1,set_meet(sK0)),
inference(paramod,[status(thm)],[c_819,c_433]) ).
cnf(c_845,negated_conjecture,
set_difference(sK1,set_meet(sK0)) != set_difference(sK1,set_meet(sK0)),
inference(paramod,[status(thm)],[c_797,c_844]) ).
cnf(c_837,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_845]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU328+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 09:18:58 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.37 % Process 1471015 was started by sandbox on n001,
% 0.03/0.37 % Sat Sep 26 09:18:58 2026
% 0.03/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.39
% 0.03/0.39 % From the command line: assign(max_seconds, 300).
% 0.86/0.56
% 0.86/0.56 % SZS status Theorem for theBenchmark
% 0.86/0.56
% 0.86/0.56 % Proof 1 at 0.09 (+ 0.06) seconds.
% 0.86/0.56 % Length of proof is 32.
% 0.86/0.56 % Level of proof is 6.
% 0.86/0.56 % Maximum clause weight is 40.000.
% 0.86/0.56 % Given clauses 150.
% 0.86/0.56
% 0.86/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------