%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU321+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 58 ( 11 unt; 8 def)
% Number of atoms : 158 ( 6 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 166 ( 66 ~; 57 |; 20 &)
% ( 10 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f191,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(the_carrier(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f264,conjecture,
! [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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f265,negated_conjecture,
~ ! [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) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f264]) ).
fof(f475,lemma,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f479,lemma,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1303,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f1337,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f201]) ).
fof(f1338,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f1337]) ).
fof(f1557,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( in(C,subset_complement(the_carrier(A),B))
<~> ~ in(C,B) )
& element(C,the_carrier(A)) )
& element(B,powerset(the_carrier(A))) )
& one_sorted_str(A)
& ~ empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f265]) ).
fof(f1558,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( in(C,B)
| ~ in(C,subset_complement(the_carrier(A),B)) )
& ( ~ 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(NNF_transformation,[status(thm)],[f1557]) ).
fof(f1559,plain,
( ( in(sK116_skl,sK115_skl)
| ~ in(sK116_skl,subset_complement(the_carrier(sK114_skl),sK115_skl)) )
& ( ~ in(sK116_skl,sK115_skl)
| in(sK116_skl,subset_complement(the_carrier(sK114_skl),sK115_skl)) )
& element(sK116_skl,the_carrier(sK114_skl))
& element(sK115_skl,powerset(the_carrier(sK114_skl)))
& one_sorted_str(sK114_skl)
& ~ empty_carrier(sK114_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114_skl,sK115_skl,sK116_skl]),skolemize(A,sK114_skl),skolemize(B,sK115_skl),skolemize(C,sK116_skl)],[f1558]) ).
fof(f1560,plain,
~ empty_carrier(sK114_skl),
inference(cnf_transformation,[status(thm)],[f1559]) ).
fof(f1561,plain,
one_sorted_str(sK114_skl),
inference(cnf_transformation,[status(thm)],[f1559]) ).
fof(f1562,plain,
element(sK115_skl,powerset(the_carrier(sK114_skl))),
inference(cnf_transformation,[status(thm)],[f1559]) ).
fof(f1563,plain,
element(sK116_skl,the_carrier(sK114_skl)),
inference(cnf_transformation,[status(thm)],[f1559]) ).
fof(f1564,plain,
( ~ in(sK116_skl,sK115_skl)
| in(sK116_skl,subset_complement(the_carrier(sK114_skl),sK115_skl)) ),
inference(cnf_transformation,[status(thm)],[f1559]) ).
fof(f1565,plain,
( in(sK116_skl,sK115_skl)
| ~ in(sK116_skl,subset_complement(the_carrier(sK114_skl),sK115_skl)) ),
inference(cnf_transformation,[status(thm)],[f1559]) ).
fof(f2519,plain,
! [A] :
( ! [B] :
( ! [C] :
( in(C,subset_complement(A,B))
| in(C,B)
| ~ element(C,A) )
| ~ element(B,powerset(A)) )
| A = empty_set ),
inference(pre_NNF_transformation,[status(thm)],[f475]) ).
fof(f2520,plain,
! [X0,X1,X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f2519]) ).
fof(f2543,plain,
! [A,B,C] :
( ~ in(B,C)
| ~ in(B,subset_complement(A,C))
| ~ element(C,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f479]) ).
fof(f2544,plain,
! [A,C] :
( ! [B] :
( ~ in(B,C)
| ~ in(B,subset_complement(A,C)) )
| ~ element(C,powerset(A)) ),
inference(miniscoping,[status(thm)],[f2543]) ).
fof(f2545,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X2,subset_complement(X1,X0))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f2544]) ).
fof(f3061,definition,
( sQ0_spl
<=> in(sK116_skl,subset_complement(the_carrier(sK114_skl),sK115_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f3062,plain,
( ~ sQ0_spl
| in(sK116_skl,subset_complement(the_carrier(sK114_skl),sK115_skl)) ),
inference(component_clause,[status(thm)],[f3061]) ).
fof(f3063,plain,
( sQ0_spl
| ~ in(sK116_skl,subset_complement(the_carrier(sK114_skl),sK115_skl)) ),
inference(component_clause,[status(thm)],[f3061]) ).
fof(f3064,definition,
( sQ1_spl
<=> in(sK116_skl,sK115_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f3067,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1564,f3061,f3064]) ).
fof(f3068,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1565,f3061,f3064]) ).
fof(f3620,plain,
( ~ sQ0_spl
| ~ in(sK116_skl,sK115_skl)
| ~ element(sK115_skl,powerset(the_carrier(sK114_skl))) ),
inference(resolution,[status(thm)],[f2545,f3062]) ).
fof(f3622,definition,
( sQ86_spl
<=> element(sK115_skl,powerset(the_carrier(sK114_skl))) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f3624,plain,
( sQ86_spl
| ~ element(sK115_skl,powerset(the_carrier(sK114_skl))) ),
inference(component_clause,[status(thm)],[f3622]) ).
fof(f3625,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f3620,f3622,f3064,f3061]) ).
fof(f3626,plain,
( sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3624,f1562]) ).
fof(f3627,plain,
sQ86_spl,
inference(contradiction_clause,[status(thm)],[f3626]) ).
fof(f3628,plain,
( sQ0_spl
| in(sK116_skl,sK115_skl)
| ~ element(sK116_skl,the_carrier(sK114_skl))
| ~ element(sK115_skl,powerset(the_carrier(sK114_skl)))
| the_carrier(sK114_skl) = empty_set ),
inference(resolution,[status(thm)],[f3063,f2520]) ).
fof(f3629,definition,
( sQ87_spl
<=> the_carrier(sK114_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f3630,plain,
( ~ sQ87_spl
| the_carrier(sK114_skl) = empty_set ),
inference(component_clause,[status(thm)],[f3629]) ).
fof(f3632,definition,
( sQ88_spl
<=> element(sK116_skl,the_carrier(sK114_skl)) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f3634,plain,
( sQ88_spl
| ~ element(sK116_skl,the_carrier(sK114_skl)) ),
inference(component_clause,[status(thm)],[f3632]) ).
fof(f3635,plain,
( sQ0_spl
| sQ1_spl
| ~ sQ88_spl
| ~ sQ86_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f3628,f3629,f3622,f3632,f3064,f3061]) ).
fof(f3693,plain,
( ~ sQ87_spl
| ~ empty(empty_set)
| ~ one_sorted_str(sK114_skl)
| empty_carrier(sK114_skl) ),
inference(paramodulation,[status(thm)],[f3630,f1338]) ).
fof(f3694,definition,
( sQ93_spl
<=> empty_carrier(sK114_skl) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f3695,plain,
( ~ sQ93_spl
| empty_carrier(sK114_skl) ),
inference(component_clause,[status(thm)],[f3694]) ).
fof(f3697,definition,
( sQ94_spl
<=> one_sorted_str(sK114_skl) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f3699,plain,
( sQ94_spl
| ~ one_sorted_str(sK114_skl) ),
inference(component_clause,[status(thm)],[f3697]) ).
fof(f3700,definition,
( sQ95_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f3702,plain,
( sQ95_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f3700]) ).
fof(f3703,plain,
( ~ sQ87_spl
| ~ sQ95_spl
| ~ sQ94_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f3693,f3694,f3697,f3700,f3629]) ).
fof(f3704,plain,
( sQ95_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3702,f1303]) ).
fof(f3705,plain,
sQ95_spl,
inference(contradiction_clause,[status(thm)],[f3704]) ).
fof(f3706,plain,
( sQ94_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3699,f1561]) ).
fof(f3707,plain,
sQ94_spl,
inference(contradiction_clause,[status(thm)],[f3706]) ).
fof(f3708,plain,
( ~ sQ93_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3695,f1560]) ).
fof(f3709,plain,
~ sQ93_spl,
inference(contradiction_clause,[status(thm)],[f3708]) ).
fof(f3807,plain,
( sQ88_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3634,f1563]) ).
fof(f3808,plain,
sQ88_spl,
inference(contradiction_clause,[status(thm)],[f3807]) ).
fof(f3809,plain,
$false,
inference(sat_refutation,[status(thm)],[f3067,f3068,f3625,f3627,f3635,f3703,f3705,f3707,f3709,f3808]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU321+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 06:11:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.42 % Drodi V4.1.1
% 0.20/0.47 % Refutation found
% 0.20/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.51 % Elapsed time: 0.141214 seconds
% 0.20/0.51 % CPU time: 0.409086 seconds
% 0.20/0.51 % Total memory used: 132.905 MB
% 0.20/0.51 % Net memory used: 132.148 MB
%------------------------------------------------------------------------------