%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU325+2 : 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 : 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 08:45:49 AM UTC 2026
% Result : Theorem 179.95s 25.06s
% Output : CNFRefutation 179.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 30 unt; 0 def)
% Number of atoms : 133 ( 40 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 104 ( 38 ~; 27 |; 24 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 6 sgn 19 !; 6 ?)
% 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(d3_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('theBenchmark.p',d3_pre_topc) ).
fof(d8_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( is_a_cover_of_carrier(A,B)
<=> cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) ) ) ),
file('theBenchmark.p',d8_pre_topc) ).
fof(dt_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k5_setfam_1) ).
fof(rc1_partfun1,axiom,
? [A] :
( empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc1_partfun1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('theBenchmark.p',redefinition_k5_setfam_1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t3_xboole_1,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t5_tops_2,conjecture,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( B = empty_set
& is_a_cover_of_carrier(A,B) ) ) ),
file('theBenchmark.p',t5_tops_2) ).
fof(t5_tops_2_neg,negated_conjecture,
~ ! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( B = empty_set
& is_a_cover_of_carrier(A,B) ) ) ),
inference(assume_negation,[status(cth)],[t5_tops_2]) ).
cnf(c_849,plain,
( ~ empty(the_carrier(A))
| empty_carrier(A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d1_struct_0]) ).
cnf(c_912,plain,
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d3_pre_topc]) ).
cnf(c_913,plain,
( the_carrier(A) = cast_as_carrier_subset(A)
| ~ one_sorted_str(A) ),
inference(copy,[status(thm)],[c_912]) ).
cnf(c_1036,plain,
( cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B)
| ~ is_a_cover_of_carrier(A,B)
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d8_pre_topc]) ).
cnf(c_1037,plain,
( union_of_subsets(the_carrier(A),B) = cast_as_carrier_subset(A)
| ~ is_a_cover_of_carrier(A,B)
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(copy,[status(thm)],[c_1036]) ).
cnf(c_1073,plain,
( element(union_of_subsets(B,A),powerset(B))
| ~ element(A,powerset(powerset(B))) ),
inference(clausify,[status(thm)],[dt_k5_setfam_1]) ).
fof(nnf_212,plain,
? [A] :
( empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_partfun1]) ).
fof(sk_rc1_partfun1,plain,
( empty(sK0)
& one_to_one(sK0)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_212]) ).
cnf(c_1283,plain,
empty(sK0),
inference(split_conjunct,[status(thm)],[sk_rc1_partfun1]) ).
fof(nnf_222,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(sk_rc2_subset_1,plain,
! [A] :
( empty(sK1(A))
& element(sK1(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(B,sK1(A))],[nnf_222]) ).
cnf(c_1316,plain,
element(sK1(A),powerset(A)),
inference(split_conjunct,[status(thm)],[sk_rc2_subset_1]) ).
cnf(c_1317,plain,
empty(sK1(A)),
inference(split_conjunct,[status(thm)],[sk_rc2_subset_1]) ).
cnf(c_1338,plain,
( union(A) = union_of_subsets(B,A)
| ~ element(A,powerset(powerset(B))) ),
inference(clausify,[status(thm)],[redefinition_k5_setfam_1]) ).
cnf(c_1339,plain,
( union_of_subsets(B,A) = union(A)
| ~ element(A,powerset(powerset(B))) ),
inference(copy,[status(thm)],[c_1338]) ).
cnf(c_3021,plain,
( subset(A,B)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_3027,plain,
( empty_set = A
| ~ subset(A,empty_set) ),
inference(clausify,[status(thm)],[t3_xboole_1]) ).
cnf(c_3132,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
fof(nnf_536,plain,
? [A] :
( ? [B] :
( empty_set = B
& is_a_cover_of_carrier(A,B)
& element(B,powerset(powerset(the_carrier(A)))) )
& one_sorted_str(A)
& ~ empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t5_tops_2_neg]) ).
fof(sk_t5_tops_2_neg,plain,
( empty_set = sK3
& is_a_cover_of_carrier(sK2,sK3)
& element(sK3,powerset(powerset(the_carrier(sK2))))
& one_sorted_str(sK2)
& ~ empty_carrier(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(A,sK2),skolemize(B,sK3)],[nnf_536]) ).
cnf(c_3172,negated_conjecture,
~ empty_carrier(sK2),
inference(split_conjunct,[status(thm)],[sk_t5_tops_2_neg]) ).
cnf(c_3173,negated_conjecture,
one_sorted_str(sK2),
inference(split_conjunct,[status(thm)],[sk_t5_tops_2_neg]) ).
cnf(c_3175,negated_conjecture,
is_a_cover_of_carrier(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t5_tops_2_neg]) ).
cnf(c_3176,negated_conjecture,
empty_set = sK3,
inference(split_conjunct,[status(thm)],[sk_t5_tops_2_neg]) ).
cnf(c_4407,plain,
( sK3 = A
| ~ empty(A) ),
inference(paramod,[status(thm)],[c_3176,c_3132]) ).
cnf(c_53018,plain,
( empty_set = A
| ~ subset(A,sK3) ),
inference(paramod,[status(thm)],[c_3176,c_3027]) ).
cnf(c_4423,plain,
( sK3 = A
| ~ subset(A,sK3) ),
inference(paramod,[status(thm)],[c_3176,c_53018]) ).
cnf(c_53019,plain,
sK3 = sK1(A),
inference(resolve,[status(thm)],[c_4407,c_1317]) ).
cnf(c_5624,plain,
sK1(A) = sK3,
inference(copy,[status(thm)],[c_53019]) ).
cnf(c_5645,plain,
element(sK3,powerset(A)),
inference(paramod,[status(thm)],[c_5624,c_1316]) ).
cnf(c_53020,negated_conjecture,
( ~ empty(the_carrier(sK2))
| empty_carrier(sK2) ),
inference(resolve,[status(thm)],[c_849,c_3173]) ).
cnf(c_6431,negated_conjecture,
~ empty(the_carrier(sK2)),
inference(resolve,[status(thm)],[c_3172,c_53020]) ).
cnf(c_6482,plain,
the_carrier(sK2) = cast_as_carrier_subset(sK2),
inference(resolve,[status(thm)],[c_913,c_3173]) ).
cnf(c_6485,negated_conjecture,
~ empty(cast_as_carrier_subset(sK2)),
inference(paramod,[status(thm)],[c_6482,c_6431]) ).
cnf(c_53021,negated_conjecture,
( union_of_subsets(the_carrier(sK2),sK3) = cast_as_carrier_subset(sK2)
| ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| ~ one_sorted_str(sK2) ),
inference(resolve,[status(thm)],[c_1037,c_3175]) ).
cnf(c_53022,negated_conjecture,
( union_of_subsets(the_carrier(sK2),sK3) = cast_as_carrier_subset(sK2)
| ~ element(sK3,powerset(powerset(cast_as_carrier_subset(sK2))))
| ~ one_sorted_str(sK2) ),
inference(paramod,[status(thm)],[c_6482,c_53021]) ).
cnf(c_53023,negated_conjecture,
( union_of_subsets(cast_as_carrier_subset(sK2),sK3) = cast_as_carrier_subset(sK2)
| ~ element(sK3,powerset(powerset(cast_as_carrier_subset(sK2))))
| ~ one_sorted_str(sK2) ),
inference(paramod,[status(thm)],[c_6482,c_53022]) ).
cnf(c_53024,negated_conjecture,
( union_of_subsets(cast_as_carrier_subset(sK2),sK3) = cast_as_carrier_subset(sK2)
| ~ element(sK3,powerset(powerset(cast_as_carrier_subset(sK2)))) ),
inference(resolve,[status(thm)],[c_3173,c_53023]) ).
cnf(c_21881,negated_conjecture,
union_of_subsets(cast_as_carrier_subset(sK2),sK3) = cast_as_carrier_subset(sK2),
inference(resolve,[status(thm)],[c_5645,c_53024]) ).
cnf(c_23622,plain,
element(union_of_subsets(A,sK3),powerset(A)),
inference(resolve,[status(thm)],[c_1073,c_5645]) ).
cnf(c_29602,plain,
subset(union_of_subsets(A,sK3),A),
inference(resolve,[status(thm)],[c_23622,c_3021]) ).
cnf(c_53025,plain,
sK3 = union_of_subsets(sK3,sK3),
inference(resolve,[status(thm)],[c_29602,c_4423]) ).
cnf(c_29654,plain,
union_of_subsets(sK3,sK3) = sK3,
inference(copy,[status(thm)],[c_53025]) ).
cnf(c_43892,plain,
sK3 = sK0,
inference(resolve,[status(thm)],[c_1283,c_4407]) ).
cnf(c_53026,plain,
union_of_subsets(sK0,sK3) = sK3,
inference(paramod,[status(thm)],[c_43892,c_29654]) ).
cnf(c_53027,plain,
union_of_subsets(sK0,sK0) = sK3,
inference(paramod,[status(thm)],[c_43892,c_53026]) ).
cnf(c_45698,plain,
union_of_subsets(sK0,sK0) = sK0,
inference(paramod,[status(thm)],[c_43892,c_53027]) ).
cnf(c_46455,negated_conjecture,
union_of_subsets(cast_as_carrier_subset(sK2),sK0) = cast_as_carrier_subset(sK2),
inference(paramod,[status(thm)],[c_43892,c_21881]) ).
cnf(c_47883,plain,
element(sK0,powerset(A)),
inference(paramod,[status(thm)],[c_43892,c_5645]) ).
cnf(c_52986,plain,
union_of_subsets(A,sK0) = union(sK0),
inference(resolve,[status(thm)],[c_47883,c_1339]) ).
cnf(c_52990,negated_conjecture,
union(sK0) = cast_as_carrier_subset(sK2),
inference(paramod,[status(thm)],[c_52986,c_46455]) ).
cnf(c_53028,plain,
union(sK0) = sK0,
inference(paramod,[status(thm)],[c_52986,c_45698]) ).
cnf(c_53012,plain,
cast_as_carrier_subset(sK2) = sK0,
inference(paramod,[status(thm)],[c_52990,c_53028]) ).
cnf(c_53029,negated_conjecture,
~ empty(sK0),
inference(paramod,[status(thm)],[c_53012,c_6485]) ).
cnf(c_53017,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1283,c_53029]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU325+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n003.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 09:14:23 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.43 % Process 2531777 was started by sandbox on n003,
% 0.14/0.43 % Sat Sep 26 09:14:23 2026
% 0.14/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.65/1.01
% 0.65/1.01 % From the command line: assign(max_seconds, 300).
% 0.65/1.01
% 0.65/1.01 % SInE: 438 to sos, 99 to usable, of 537 axioms (tolerance 2.00, depth 0 fixpoint).
% 179.95/25.06
% 179.95/25.06 % given #500 (T,wt=7): 6573 empty(A) | -finite(A) | finite(f103(A)). [resolve(1286,b,730,b)].
% 179.95/25.06
% 179.95/25.06 % given #1000 (W,wt=6): 8353 -v1_membered(A) | v1_membered(f35(powerset(A))). [back_unit_del(6770),unit_del(a,8306)].
% 179.95/25.06
% 179.95/25.06 % given #1500 (F,wt=12): 9699 set_difference(A,powerset(pair_second(ordered_pair(B,C)))) != D | -in(C,D). [resolve(8290,a,966,c)].
% 179.95/25.06
% 179.95/25.06 % given #2000 (T,wt=7): 13892 ordinal(f316(pair_second(ordered_pair(A,powerset(c32))))). [resolve(11509,a,670,b),unit_del(a,4667)].
% 179.95/25.06
% 179.95/25.06 % given #2500 (F,wt=7): 18646 -in(pair_first(ordered_pair(omega,A)),f90(omega)). [resolve(17822,a,698,b)].
% 179.95/25.06
% 179.95/25.06 % given #3000 (T,wt=7): 21511 one_to_one(c30) | -in(relation_dom(c30),f80(c30)). [resolve(21454,b,698,b)].
% 179.95/25.06
% 179.95/25.06 % given #3500 (F,wt=11): 15533 set_difference(A,pair_first(ordered_pair(singleton(f316(omega)),B))) != powerset(omega). [resolve(12456,b,11558,a)].
% 179.95/25.06
% 179.95/25.06 % given #4000 (T,wt=4): 34085 epsilon_transitive(union(union(c32))). [resolve(34061,a,1182,a)].
% 179.95/25.06
% 179.95/25.06 % given #4500 (A,wt=210): 1247 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(B,D) # tptp_name(l55_zfmisc_1) # sine_depth(3). [clausify(202)].
% 179.95/25.06
% 179.95/25.06 % given #5000 (T,wt=3): 48118 v1_xcmplx_0(f90(c11)). [resolve(47995,a,5551,a)].
% 179.95/25.06
% 179.95/25.06 % given #5500 (W,wt=3): 51361 v5_membered(relation_dom(c14)). [resolve(49453,a,703,a)].
% 179.95/25.06
% 179.95/25.06 % SZS status Theorem for theBenchmark
% 179.95/25.06
% 179.95/25.06 % Proof 1 at 20.81 (+ 2.59) seconds.
% 179.95/25.06 % Length of proof is 48.
% 179.95/25.06 % Level of proof is 10.
% 179.95/25.06 % Maximum clause weight is 202.000.
% 179.95/25.06 % Given clauses 5619.
% 179.95/25.06
% 179.95/25.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------