%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET028-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:08:59 PM UTC 2026
% Result : Unsatisfiable 1.19s 0.76s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 61 ( 11 unt; 5 def)
% Number of atoms : 139 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 151 ( 73 ~; 73 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 71 ( 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f65,axiom,
! [Z,X,Y] :
( ~ member(Z,Y)
| ~ member(Y,X)
| member(Z,sigma(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [X,Y] :
( member(f17(X,Y),X)
| subset(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [X,Y] :
( ~ member(f17(X,Y),Y)
| subset(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [Z,X,Xf,Y] :
( second(Y) != Z
| ~ member(first(Y),X)
| ~ member(Y,Xf)
| ~ ordered_pair_predicate(Y)
| ~ little_set(Z)
| member(Z,image(X,Xf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,axiom,
! [Z,Xf,Y] :
( ordered_pair_predicate(f28(Z,Xf,Y))
| ~ member(Z,apply(Xf,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,axiom,
! [Z,Xf,Y] :
( member(f28(Z,Xf,Y),Xf)
| ~ member(Z,apply(Xf,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,axiom,
! [Z,Xf,Y] :
( first(f28(Z,Xf,Y)) = Y
| ~ member(Z,apply(Xf,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f117,axiom,
! [Z,Xf,Y] :
( member(Z,second(f28(Z,Xf,Y)))
| ~ member(Z,apply(Xf,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f148,axiom,
! [X] :
( little_set(first(X))
| ~ ordered_pair_predicate(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f149,axiom,
! [X] :
( little_set(second(X))
| ~ ordered_pair_predicate(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f150,axiom,
! [X] :
( member(X,singleton_set(X))
| ~ little_set(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f154,negated_conjecture,
~ subset(apply(a_function,element),sigma(image(singleton_set(element),a_function))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f236,plain,
! [Z,Y] :
( ~ member(Z,Y)
| ! [X] :
( ~ member(Y,X)
| member(Z,sigma(X)) ) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f237,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X2,X1)
| member(X0,sigma(X1)) ),
inference(cnf_transformation,[status(thm)],[f236]) ).
fof(f241,plain,
! [X0,X1] :
( member(f17(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f242,plain,
! [X0,X1] :
( ~ member(f17(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f268,plain,
! [Z,Y] :
( second(Y) != Z
| ! [X] :
( ~ member(first(Y),X)
| ! [Xf] :
( ~ member(Y,Xf)
| ~ ordered_pair_predicate(Y)
| ~ little_set(Z)
| member(Z,image(X,Xf)) ) ) ),
inference(miniscoping,[status(thm)],[f93]) ).
fof(f269,plain,
! [X0,X1,X2,X3] :
( second(X3) != X0
| ~ member(first(X3),X1)
| ~ member(X3,X2)
| ~ ordered_pair_predicate(X3)
| ~ little_set(X0)
| member(X0,image(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f268]) ).
fof(f292,plain,
! [X0,X1,X2] :
( ordered_pair_predicate(f28(X0,X1,X2))
| ~ member(X0,apply(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f293,plain,
! [X0,X1,X2] :
( member(f28(X0,X1,X2),X1)
| ~ member(X0,apply(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f294,plain,
! [X0,X1,X2] :
( first(f28(X0,X1,X2)) = X2
| ~ member(X0,apply(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f295,plain,
! [X0,X1,X2] :
( member(X0,second(f28(X0,X1,X2)))
| ~ member(X0,apply(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f341,plain,
! [X0] :
( little_set(first(X0))
| ~ ordered_pair_predicate(X0) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f342,plain,
! [X0] :
( little_set(second(X0))
| ~ ordered_pair_predicate(X0) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f343,plain,
! [X0] :
( member(X0,singleton_set(X0))
| ~ little_set(X0) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f348,plain,
~ subset(apply(a_function,element),sigma(image(singleton_set(element),a_function))),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f358,plain,
! [X0,X1,X2] :
( ~ member(first(X0),X1)
| ~ member(X0,X2)
| ~ ordered_pair_predicate(X0)
| ~ little_set(second(X0))
| member(second(X0),image(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f269]) ).
fof(f1110,plain,
! [X0] :
( member(first(X0),singleton_set(first(X0)))
| ~ ordered_pair_predicate(X0) ),
inference(resolution,[status(thm)],[f341,f343]) ).
fof(f1111,plain,
! [X0,X1,X2] :
( ~ member(first(X0),X1)
| ~ member(X0,X2)
| ~ ordered_pair_predicate(X0)
| member(second(X0),image(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[f358,f342]) ).
fof(f1248,plain,
member(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),apply(a_function,element)),
inference(resolution,[status(thm)],[f241,f348]) ).
fof(f1327,plain,
! [X0,X1,X2] :
( ~ member(f17(X0,sigma(X1)),X2)
| ~ member(X2,X1)
| subset(X0,sigma(X1)) ),
inference(resolution,[status(thm)],[f242,f237]) ).
fof(f1779,plain,
! [X0] :
( ~ member(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),X0)
| ~ member(X0,image(singleton_set(element),a_function)) ),
inference(resolution,[status(thm)],[f1327,f348]) ).
fof(f1858,plain,
! [X0] :
( ~ member(first(X0),singleton_set(element))
| ~ member(X0,a_function)
| ~ ordered_pair_predicate(X0)
| ~ member(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),second(X0)) ),
inference(resolution,[status(thm)],[f1779,f1111]) ).
fof(f2046,plain,
ordered_pair_predicate(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element)),
inference(resolution,[status(thm)],[f292,f1248]) ).
fof(f2053,plain,
member(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element),a_function),
inference(resolution,[status(thm)],[f293,f1248]) ).
fof(f2097,plain,
first(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element)) = element,
inference(resolution,[status(thm)],[f294,f1248]) ).
fof(f2104,plain,
member(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),second(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element))),
inference(resolution,[status(thm)],[f295,f1248]) ).
fof(f2184,plain,
( member(element,singleton_set(first(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element))))
| ~ ordered_pair_predicate(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element)) ),
inference(paramodulation,[status(thm)],[f2097,f1110]) ).
fof(f2188,definition,
( sQ58_spl
<=> ordered_pair_predicate(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element)) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f2190,plain,
( sQ58_spl
| ~ ordered_pair_predicate(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element)) ),
inference(component_clause,[status(thm)],[f2188]) ).
fof(f2195,definition,
( sQ60_spl
<=> member(element,singleton_set(first(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element)))) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f2196,plain,
( ~ sQ60_spl
| member(element,singleton_set(first(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element)))) ),
inference(component_clause,[status(thm)],[f2195]) ).
fof(f2198,plain,
( sQ60_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f2184,f2188,f2195]) ).
fof(f2207,plain,
( sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2190,f2046]) ).
fof(f2208,plain,
sQ58_spl,
inference(contradiction_clause,[status(thm)],[f2207]) ).
fof(f2209,plain,
( ~ sQ60_spl
| member(element,singleton_set(element)) ),
inference(forward_demodulation,[status(thm)],[f2097,f2196]) ).
fof(f2342,plain,
( ~ member(element,singleton_set(element))
| ~ member(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element),a_function)
| ~ ordered_pair_predicate(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element))
| ~ member(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),second(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element))) ),
inference(paramodulation,[status(thm)],[f2097,f1858]) ).
fof(f2343,definition,
( sQ63_spl
<=> member(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),second(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element))) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f2345,plain,
( sQ63_spl
| ~ member(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),second(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element))) ),
inference(component_clause,[status(thm)],[f2343]) ).
fof(f2346,definition,
( sQ64_spl
<=> member(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element),a_function) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f2348,plain,
( sQ64_spl
| ~ member(f28(f17(apply(a_function,element),sigma(image(singleton_set(element),a_function))),a_function,element),a_function) ),
inference(component_clause,[status(thm)],[f2346]) ).
fof(f2349,definition,
( sQ65_spl
<=> member(element,singleton_set(element)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f2351,plain,
( sQ65_spl
| ~ member(element,singleton_set(element)) ),
inference(component_clause,[status(thm)],[f2349]) ).
fof(f2352,plain,
( ~ sQ65_spl
| ~ sQ64_spl
| ~ sQ58_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f2342,f2343,f2188,f2346,f2349]) ).
fof(f2353,plain,
( sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2348,f2053]) ).
fof(f2354,plain,
sQ64_spl,
inference(contradiction_clause,[status(thm)],[f2353]) ).
fof(f2355,plain,
( sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2345,f2104]) ).
fof(f2356,plain,
sQ63_spl,
inference(contradiction_clause,[status(thm)],[f2355]) ).
fof(f3018,plain,
( sQ65_spl
| ~ sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2351,f2209]) ).
fof(f3019,plain,
( sQ65_spl
| ~ sQ60_spl ),
inference(contradiction_clause,[status(thm)],[f3018]) ).
fof(f3020,plain,
$false,
inference(sat_refutation,[status(thm)],[f2198,f2208,f2352,f2354,f2356,f3019]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET028-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n011.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 04:44:25 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 1.19/0.76 % Refutation found
% 1.19/0.76 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.19/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.72/0.79 % Elapsed time: 0.422614 seconds
% 2.72/0.79 % CPU time: 3.038269 seconds
% 2.72/0.79 % Total memory used: 148.255 MB
% 2.72/0.79 % Net memory used: 143.805 MB
%------------------------------------------------------------------------------