%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU325+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 : Thu Sep 24 02:20:10 PM UTC 2026
% Result : Theorem 28.04s 4.04s
% Output : CNFRefutation 28.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 22 unt; 0 def)
% Number of atoms : 169 ( 40 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 158 ( 57 ~; 45 |; 42 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 68 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f113,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('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f160,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f215,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(cast_as_carrier_subset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f287,axiom,
? [A] :
( empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f292,axiom,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f313,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f457,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f460,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f498,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('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f499,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(negated_conjecture,[status(cth)],[f498]) ).
fof(f511,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f527,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1181,plain,
! [A] :
( ! [B] :
( ( is_a_cover_of_carrier(A,B)
<=> cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) )
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f113]) ).
fof(f1182,plain,
! [A] :
( ! [B] :
( ( ( cast_as_carrier_subset(A) != union_of_subsets(the_carrier(A),B)
| is_a_cover_of_carrier(A,B) )
& ( 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(NNF_transformation,[status(thm)],[f1181]) ).
fof(f1183,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ is_a_cover_of_carrier(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| union_of_subsets(the_carrier(X0),X1) = cast_as_carrier_subset(X0) ),
inference(cnf_transformation,[status(thm)],[f1182]) ).
fof(f1259,plain,
! [A,B] :
( element(union_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f160]) ).
fof(f1260,plain,
! [X0,X1] :
( element(union_of_subsets(X1,X0),powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f1259]) ).
fof(f1396,plain,
! [A] :
( ~ empty(cast_as_carrier_subset(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f215]) ).
fof(f1397,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f1396]) ).
fof(f1662,plain,
( empty(sK124_skl)
& one_to_one(sK124_skl)
& function(sK124_skl)
& relation(sK124_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124_skl]),skolemize(A,sK124_skl)],[f287]) ).
fof(f1666,plain,
empty(sK124_skl),
inference(cnf_transformation,[status(thm)],[f1662]) ).
fof(f1680,plain,
! [A] :
( finite(sK129_skl(A))
& natural(sK129_skl(A))
& ordinal(sK129_skl(A))
& epsilon_connected(sK129_skl(A))
& epsilon_transitive(sK129_skl(A))
& one_to_one(sK129_skl(A))
& function(sK129_skl(A))
& relation(sK129_skl(A))
& empty(sK129_skl(A))
& element(sK129_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129_skl]),skolemize(B,sK129_skl(A))],[f292]) ).
fof(f1681,plain,
! [X0] : element(sK129_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f1680]) ).
fof(f1682,plain,
! [X0] : empty(sK129_skl(X0)),
inference(cnf_transformation,[status(thm)],[f1680]) ).
fof(f1762,plain,
! [A,B] :
( union_of_subsets(A,B) = union(B)
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f313]) ).
fof(f1763,plain,
! [X0,X1] :
( union(X0) = union_of_subsets(X1,X0)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f1762]) ).
fof(f2469,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f457]) ).
fof(f2470,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f2469]) ).
fof(f2471,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f2470]) ).
fof(f2480,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f460]) ).
fof(f2481,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(thm)],[f2480]) ).
fof(f2609,plain,
? [A] :
( ? [B] :
( B = empty_set
& is_a_cover_of_carrier(A,B)
& element(B,powerset(powerset(the_carrier(A)))) )
& one_sorted_str(A)
& ~ empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f499]) ).
fof(f2610,plain,
( sK305_skl = empty_set
& is_a_cover_of_carrier(sK304_skl,sK305_skl)
& element(sK305_skl,powerset(powerset(the_carrier(sK304_skl))))
& one_sorted_str(sK304_skl)
& ~ empty_carrier(sK304_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK304_skl,sK305_skl]),skolemize(A,sK304_skl),skolemize(B,sK305_skl)],[f2609]) ).
fof(f2611,plain,
~ empty_carrier(sK304_skl),
inference(cnf_transformation,[status(thm)],[f2610]) ).
fof(f2612,plain,
one_sorted_str(sK304_skl),
inference(cnf_transformation,[status(thm)],[f2610]) ).
fof(f2613,plain,
element(sK305_skl,powerset(powerset(the_carrier(sK304_skl)))),
inference(cnf_transformation,[status(thm)],[f2610]) ).
fof(f2614,plain,
is_a_cover_of_carrier(sK304_skl,sK305_skl),
inference(cnf_transformation,[status(thm)],[f2610]) ).
fof(f2615,plain,
empty_set = sK305_skl,
inference(cnf_transformation,[status(thm)],[f2610]) ).
fof(f2650,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f511]) ).
fof(f2651,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f2650]) ).
fof(f2701,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f527]) ).
fof(f2702,plain,
! [B] :
( ~ empty(B)
| ! [A] :
( A = B
| ~ empty(A) ) ),
inference(miniscoping,[status(thm)],[f2701]) ).
fof(f2703,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f2702]) ).
fof(f3227,plain,
( ~ one_sorted_str(sK304_skl)
| ~ is_a_cover_of_carrier(sK304_skl,sK305_skl)
| union_of_subsets(the_carrier(sK304_skl),sK305_skl) = cast_as_carrier_subset(sK304_skl) ),
inference(resolution,[status(thm)],[f1183,f2613]) ).
fof(f3229,plain,
( ~ one_sorted_str(sK304_skl)
| cast_as_carrier_subset(sK304_skl) = union_of_subsets(the_carrier(sK304_skl),sK305_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f3227,f2614]) ).
fof(f3230,plain,
cast_as_carrier_subset(sK304_skl) = union_of_subsets(the_carrier(sK304_skl),sK305_skl),
inference(forward_subsumption_resolution,[status(thm)],[f3229,f2612]) ).
fof(f3261,plain,
! [X0] :
( X0 = sK305_skl
| ~ empty(X0) ),
inference(forward_demodulation,[status(thm)],[f2615,f2651]) ).
fof(f3387,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,sK305_skl) ),
inference(forward_demodulation,[status(thm)],[f2615,f2481]) ).
fof(f3388,plain,
! [X0] :
( X0 = sK305_skl
| ~ subset(X0,sK305_skl) ),
inference(forward_demodulation,[status(thm)],[f2615,f3387]) ).
fof(f4022,plain,
union(sK305_skl) = union_of_subsets(the_carrier(sK304_skl),sK305_skl),
inference(resolution,[status(thm)],[f1763,f2613]) ).
fof(f4029,plain,
union(sK305_skl) = cast_as_carrier_subset(sK304_skl),
inference(forward_demodulation,[status(thm)],[f3230,f4022]) ).
fof(f5288,plain,
! [X0] :
( ~ empty(X0)
| X0 = sK124_skl ),
inference(resolution,[status(thm)],[f1666,f2703]) ).
fof(f5289,plain,
sK124_skl = sK305_skl,
inference(resolution,[status(thm)],[f1666,f3261]) ).
fof(f5399,plain,
union(sK124_skl) = cast_as_carrier_subset(sK304_skl),
inference(backward_demodulation,[status(thm)],[f5289,f4029]) ).
fof(f5422,plain,
! [X0] :
( X0 = sK124_skl
| ~ subset(X0,sK305_skl) ),
inference(backward_demodulation,[status(thm)],[f5289,f3388]) ).
fof(f5501,plain,
! [X0] :
( ~ subset(X0,sK124_skl)
| sK124_skl = X0 ),
inference(forward_demodulation,[status(thm)],[f5289,f5422]) ).
fof(f7004,plain,
! [X0] : sK124_skl = sK129_skl(X0),
inference(resolution,[status(thm)],[f1682,f5288]) ).
fof(f7020,plain,
! [X0] : element(sK124_skl,powerset(X0)),
inference(backward_demodulation,[status(thm)],[f7004,f1681]) ).
fof(f7030,plain,
! [X0] : union(sK124_skl) = union_of_subsets(X0,sK124_skl),
inference(resolution,[status(thm)],[f7020,f1763]) ).
fof(f7042,plain,
! [X0] : union_of_subsets(X0,sK124_skl) = cast_as_carrier_subset(sK304_skl),
inference(forward_demodulation,[status(thm)],[f5399,f7030]) ).
fof(f7070,plain,
! [X0] :
( element(cast_as_carrier_subset(sK304_skl),powerset(X0))
| ~ element(sK124_skl,powerset(powerset(X0))) ),
inference(paramodulation,[status(thm)],[f7042,f1260]) ).
fof(f7073,plain,
! [X0] : element(cast_as_carrier_subset(sK304_skl),powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f7070,f7020]) ).
fof(f7090,plain,
! [X0] : subset(cast_as_carrier_subset(sK304_skl),X0),
inference(resolution,[status(thm)],[f7073,f2471]) ).
fof(f7183,plain,
sK124_skl = cast_as_carrier_subset(sK304_skl),
inference(resolution,[status(thm)],[f7090,f5501]) ).
fof(f7261,plain,
( ~ empty(sK124_skl)
| empty_carrier(sK304_skl)
| ~ one_sorted_str(sK304_skl) ),
inference(paramodulation,[status(thm)],[f7183,f1397]) ).
fof(f7262,plain,
( empty_carrier(sK304_skl)
| ~ empty(sK124_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f7261,f2612]) ).
fof(f7467,plain,
empty_carrier(sK304_skl),
inference(forward_subsumption_resolution,[status(thm)],[f7262,f1666]) ).
fof(f7468,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f2611,f7467]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU325+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 06:14:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.14/0.43 % Drodi V4.1.1
% 28.04/4.04 % Refutation found
% 28.04/4.04 % SZS status Theorem for theBenchmark: Theorem is valid
% 28.04/4.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.13/4.10 % Elapsed time: 3.720149 seconds
% 1.13/4.10 % CPU time: 28.750462 seconds
% 1.13/4.10 % Total memory used: 316.549 MB
% 1.13/4.10 % Net memory used: 293.533 MB
%------------------------------------------------------------------------------