%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU322+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 : n016.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 08:45:48 AM UTC 2026
% Result : Theorem 214.84s 28.61s
% Output : CNFRefutation 214.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 23 unt; 0 def)
% Number of atoms : 179 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 173 ( 69 ~; 64 |; 16 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 100 ( 1 sgn 47 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_struct_0,axiom,
! [A] :
( one_sorted_str(A)
=> ( empty_carrier(A)
<=> empty(the_carrier(A)) ) ),
file('theBenchmark.p',d1_struct_0) ).
fof(d1_tops_1,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) ) ),
file('theBenchmark.p',d1_tops_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(dt_k1_tops_1,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A) )
=> element(interior(A,B),powerset(the_carrier(A))) ),
file('theBenchmark.p',dt_k1_tops_1) ).
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(dt_k6_pre_topc,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A) )
=> element(topstr_closure(A,B),powerset(the_carrier(A))) ),
file('theBenchmark.p',dt_k6_pre_topc) ).
fof(dt_l1_pre_topc,axiom,
! [A] :
( top_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_pre_topc) ).
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(l40_tops_1,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( element(C,the_carrier(A))
=> ( in(C,subset_complement(the_carrier(A),B))
<=> ~ in(C,B) ) ) ) ),
file('theBenchmark.p',l40_tops_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t48_pre_topc,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset(B,topstr_closure(A,B)) ) ),
file('theBenchmark.p',t48_pre_topc) ).
fof(t54_subset_1,axiom,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('theBenchmark.p',t54_subset_1) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t44_tops_1,conjecture,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset(interior(A,B),B) ) ),
file('theBenchmark.p',t44_tops_1) ).
fof(t44_tops_1_neg,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset(interior(A,B),B) ) ),
inference(assume_negation,[status(cth)],[t44_tops_1]) ).
cnf(c_54,plain,
( in(C,B)
| in(C,subset_complement(the_carrier(A),B))
| ~ element(C,the_carrier(A))
| ~ element(B,powerset(the_carrier(A)))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[l40_tops_1]) ).
cnf(c_58,plain,
( one_sorted_str(A)
| ~ top_str(A) ),
inference(clausify,[status(thm)],[dt_l1_pre_topc]) ).
cnf(c_60,plain,
( empty(the_carrier(A))
| ~ empty_carrier(A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d1_struct_0]) ).
cnf(c_62,plain,
( element(topstr_closure(A,B),powerset(the_carrier(A)))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(clausify,[status(thm)],[dt_k6_pre_topc]) ).
cnf(c_63,plain,
( element(interior(A,B),powerset(the_carrier(A)))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(clausify,[status(thm)],[dt_k1_tops_1]) ).
cnf(c_64,plain,
( subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) = interior(A,B)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(clausify,[status(thm)],[d1_tops_1]) ).
cnf(c_67,plain,
( in(C,B)
| in(C,subset_complement(the_carrier(A),B))
| ~ element(C,the_carrier(A))
| ~ element(B,powerset(the_carrier(A)))
| empty_carrier(A)
| ~ top_str(A) ),
inference(resolve,[status(thm)],[c_58,c_54]) ).
cnf(c_70,plain,
( ~ top_str(A)
| empty(the_carrier(A))
| ~ empty_carrier(A) ),
inference(resolve,[status(thm)],[c_60,c_58]) ).
cnf(c_71,plain,
( subset(B,topstr_closure(A,B))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(clausify,[status(thm)],[t48_pre_topc]) ).
fof(nnf_50,plain,
? [A] :
( ? [B] :
( ~ subset(interior(A,B),B)
& element(B,powerset(the_carrier(A))) )
& top_str(A) ),
inference(fof_nnf,[status(thm)],[t44_tops_1_neg]) ).
fof(sk_t44_tops_1_neg,plain,
( ~ subset(interior(sK0,sK1),sK1)
& 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_50]) ).
cnf(c_72,negated_conjecture,
top_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t44_tops_1_neg]) ).
cnf(c_73,negated_conjecture,
( empty(the_carrier(sK0))
| ~ empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_72,c_70]) ).
cnf(c_76,negated_conjecture,
( in(B,A)
| in(B,subset_complement(the_carrier(sK0),A))
| ~ element(B,the_carrier(sK0))
| ~ element(A,powerset(the_carrier(sK0)))
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_72,c_67]) ).
cnf(c_79,negated_conjecture,
( subset_complement(the_carrier(sK0),topstr_closure(sK0,subset_complement(the_carrier(sK0),A))) = interior(sK0,A)
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_72,c_64]) ).
cnf(c_80,negated_conjecture,
( element(interior(sK0,A),powerset(the_carrier(sK0)))
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_72,c_63]) ).
cnf(c_81,negated_conjecture,
( element(topstr_closure(sK0,A),powerset(the_carrier(sK0)))
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_72,c_62]) ).
cnf(c_82,negated_conjecture,
( subset(A,topstr_closure(sK0,A))
| ~ element(A,powerset(the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_72,c_71]) ).
cnf(c_92,negated_conjecture,
~ subset(interior(sK0,sK1),sK1),
inference(split_conjunct,[status(thm)],[sk_t44_tops_1_neg]) ).
cnf(c_93,negated_conjecture,
element(sK1,powerset(the_carrier(sK0))),
inference(split_conjunct,[status(thm)],[sk_t44_tops_1_neg]) ).
cnf(c_97,plain,
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t5_subset]) ).
cnf(c_98,plain,
( ~ in(C,A)
| ~ in(C,subset_complement(B,A))
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t54_subset_1]) ).
cnf(c_101,plain,
( subset(A,B)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_103,plain,
( element(A,B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t1_subset]) ).
cnf(c_112,plain,
( subset_complement(B,subset_complement(B,A)) = A
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[involutiveness_k3_subset_1]) ).
cnf(c_120,plain,
( element(subset_complement(B,A),powerset(B))
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[dt_k3_subset_1]) ).
fof(nnf_19,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK2(A,B),B)
& in(sK2(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(C,sK2(A,B))],[nnf_19]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK2(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK2(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_121,plain,
( ~ in(sK2(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_122,plain,
( in(sK2(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_123,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_177,plain,
element(interior(sK0,sK1),powerset(the_carrier(sK0))),
inference(resolve,[status(thm)],[c_93,c_80]) ).
cnf(c_178,plain,
subset_complement(the_carrier(sK0),topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1))) = interior(sK0,sK1),
inference(resolve,[status(thm)],[c_93,c_79]) ).
cnf(c_179,plain,
( in(A,sK1)
| in(A,subset_complement(the_carrier(sK0),sK1))
| ~ element(A,the_carrier(sK0))
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_93,c_76]) ).
cnf(c_209,plain,
element(subset_complement(the_carrier(sK0),sK1),powerset(the_carrier(sK0))),
inference(resolve,[status(thm)],[c_120,c_93]) ).
cnf(c_212,negated_conjecture,
~ in(sK2(interior(sK0,sK1),sK1),sK1),
inference(resolve,[status(thm)],[c_121,c_92]) ).
cnf(c_214,plain,
in(sK2(interior(sK0,sK1),sK1),interior(sK0,sK1)),
inference(resolve,[status(thm)],[c_122,c_92]) ).
cnf(c_509,plain,
subset(interior(sK0,sK1),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_177,c_101]) ).
cnf(c_587,plain,
( in(A,the_carrier(sK0))
| ~ in(A,interior(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_509,c_123]) ).
cnf(c_871,plain,
subset(subset_complement(the_carrier(sK0),sK1),topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1))),
inference(resolve,[status(thm)],[c_209,c_82]) ).
cnf(c_872,plain,
element(topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),powerset(the_carrier(sK0))),
inference(resolve,[status(thm)],[c_209,c_81]) ).
cnf(c_20651,plain,
( ~ in(A,interior(sK0,sK1))
| ~ in(A,subset_complement(the_carrier(sK0),interior(sK0,sK1))) ),
inference(resolve,[status(thm)],[c_98,c_177]) ).
cnf(c_977,plain,
~ in(sK2(interior(sK0,sK1),sK1),subset_complement(the_carrier(sK0),interior(sK0,sK1))),
inference(resolve,[status(thm)],[c_20651,c_214]) ).
cnf(c_20652,plain,
( ~ empty(A)
| ~ element(interior(sK0,sK1),powerset(A)) ),
inference(resolve,[status(thm)],[c_97,c_214]) ).
cnf(c_979,plain,
~ empty(the_carrier(sK0)),
inference(resolve,[status(thm)],[c_20652,c_177]) ).
cnf(c_982,negated_conjecture,
~ empty_carrier(sK0),
inference(resolve,[status(thm)],[c_979,c_73]) ).
cnf(c_1096,negated_conjecture,
( in(A,sK1)
| in(A,subset_complement(the_carrier(sK0),sK1))
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_982,c_179]) ).
cnf(c_1558,plain,
in(sK2(interior(sK0,sK1),sK1),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_587,c_214]) ).
cnf(c_4384,plain,
element(sK2(interior(sK0,sK1),sK1),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_1558,c_103]) ).
cnf(c_20653,plain,
subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)))) = topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),
inference(resolve,[status(thm)],[c_872,c_112]) ).
cnf(c_20654,plain,
subset_complement(the_carrier(sK0),interior(sK0,sK1)) = topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)),
inference(paramod,[status(thm)],[c_178,c_20653]) ).
cnf(c_11732,plain,
topstr_closure(sK0,subset_complement(the_carrier(sK0),sK1)) = subset_complement(the_carrier(sK0),interior(sK0,sK1)),
inference(copy,[status(thm)],[c_20654]) ).
cnf(c_11740,plain,
subset(subset_complement(the_carrier(sK0),sK1),subset_complement(the_carrier(sK0),interior(sK0,sK1))),
inference(paramod,[status(thm)],[c_11732,c_871]) ).
cnf(c_20655,plain,
( in(sK2(interior(sK0,sK1),sK1),sK1)
| in(sK2(interior(sK0,sK1),sK1),subset_complement(the_carrier(sK0),sK1)) ),
inference(resolve,[status(thm)],[c_1096,c_4384]) ).
cnf(c_17344,plain,
in(sK2(interior(sK0,sK1),sK1),subset_complement(the_carrier(sK0),sK1)),
inference(resolve,[status(thm)],[c_212,c_20655]) ).
cnf(c_20656,plain,
( in(sK2(interior(sK0,sK1),sK1),A)
| ~ subset(subset_complement(the_carrier(sK0),sK1),A) ),
inference(resolve,[status(thm)],[c_123,c_17344]) ).
cnf(c_20657,plain,
~ subset(subset_complement(the_carrier(sK0),sK1),subset_complement(the_carrier(sK0),interior(sK0,sK1))),
inference(resolve,[status(thm)],[c_20656,c_977]) ).
cnf(c_20650,plain,
$false,
inference(resolve,[status(thm)],[c_11740,c_20657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU322+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n016.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 09:16:46 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 534856 was started by sandbox on n016,
% 0.19/0.44 % Sat Sep 26 09:16:46 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 214.84/28.61
% 214.84/28.61 % given #500 (F,wt=21): 1546 -in(c3,powerset(f1(c3,empty_set))). [ur(103,b,1508,a)].
% 214.84/28.61
% 214.84/28.61 % given #1000 (A,wt=31): 538 element(topstr_closure(c5,subset_complement(the_carrier(c5),the_carrier(c5))),powerset(the_carrier(c5))). [resolve(339,a,81,a)].
% 214.84/28.61
% 214.84/28.61 % given #1500 (T,wt=21): 6261 element(f1(A,empty_set),A) | -v3_membered(B) | v3_membered(subset_complement(B,A)). [resolve(5499,b,137,b)].
% 214.84/28.61
% 214.84/28.61 % given #2000 (F,wt=30): 10271 -in(the_carrier(c5),powerset(f1(the_carrier(c5),subset_complement(c6,c6)))). [ur(103,b,9162,a)].
% 214.84/28.61
% 214.84/28.61 % given #2500 (A,wt=44): 1010 in(f2(the_carrier(c5)),subset_complement(the_carrier(c5),f2(powerset(the_carrier(c5))))) | in(f2(the_carrier(c5)),f2(powerset(the_carrier(c5)))). [back_unit_del(806),unit_del(a,982)].
% 214.84/28.61
% 214.84/28.61 % given #3000 (T,wt=25): 5779 v4_membered(powerset(A)) | -v4_membered(A) | v3_membered(f1(powerset(A),empty_set)). [resolve(5746,a,134,b)].
% 214.84/28.61
% 214.84/28.61 % SZS status Theorem for theBenchmark
% 214.84/28.61
% 214.84/28.61 % Proof 1 at 3.00 (+ 0.95) seconds.
% 214.84/28.61 % Length of proof is 62.
% 214.84/28.61 % Level of proof is 9.
% 214.84/28.61 % Maximum clause weight is 43.000.
% 214.84/28.61 % Given clauses 3288.
% 214.84/28.61
% 214.84/28.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------