%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 02:10:34 PM UTC 2026
% Result : Theorem 0.14s 5.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 6 unt; 2 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 41 ~; 38 |; 21 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 74 ( 63 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [F,B,X] :
( member(X,inverse_image2(F,B))
<=> ? [Y] :
( apply(F,X,Y)
& member(Y,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [F,A,B] :
( maps(F,A,B)
=> equal_set(inverse_image2(F,empty_set),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [F,A,B] :
( maps(F,A,B)
=> equal_set(inverse_image2(F,empty_set),empty_set) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f32,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f33]) ).
fof(f36,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f39,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f42,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f57,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f189,plain,
! [F,B,X] :
( ( ! [Y] :
( ~ apply(F,X,Y)
| ~ member(Y,B) )
| member(X,inverse_image2(F,B)) )
& ( ? [Y] :
( apply(F,X,Y)
& member(Y,B) )
| ~ member(X,inverse_image2(F,B)) ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f190,plain,
( ! [F,B,X] :
( ! [Y] :
( ~ apply(F,X,Y)
| ~ member(Y,B) )
| member(X,inverse_image2(F,B)) )
& ! [F,B,X] :
( ? [Y] :
( apply(F,X,Y)
& member(Y,B) )
| ~ member(X,inverse_image2(F,B)) ) ),
inference(miniscoping,[status(thm)],[f189]) ).
fof(f191,plain,
( ! [F,B,X] :
( ! [Y] :
( ~ apply(F,X,Y)
| ~ member(Y,B) )
| member(X,inverse_image2(F,B)) )
& ! [F,B,X] :
( ( apply(F,X,sK25_skl(X,B,F))
& member(sK25_skl(X,B,F),B) )
| ~ member(X,inverse_image2(F,B)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl]),skolemize(Y,sK25_skl(X,B,F))],[f190]) ).
fof(f192,plain,
! [X0,X1,X2] :
( member(sK25_skl(X0,X2,X1),X2)
| ~ member(X0,inverse_image2(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f244,plain,
? [F,A,B] :
( ~ equal_set(inverse_image2(F,empty_set),empty_set)
& maps(F,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f245,plain,
? [F] :
( ~ equal_set(inverse_image2(F,empty_set),empty_set)
& ? [A,B] : maps(F,A,B) ),
inference(miniscoping,[status(thm)],[f244]) ).
fof(f246,plain,
( ~ equal_set(inverse_image2(sK39_skl,empty_set),empty_set)
& maps(sK39_skl,sK40_skl,sK41_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39_skl,sK40_skl,sK41_skl]),skolemize(F,sK39_skl),skolemize(A,sK40_skl),skolemize(B,sK41_skl)],[f245]) ).
fof(f248,plain,
~ equal_set(inverse_image2(sK39_skl,empty_set),empty_set),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f265,plain,
( ~ subset(empty_set,inverse_image2(sK39_skl,empty_set))
| ~ subset(inverse_image2(sK39_skl,empty_set),empty_set) ),
inference(resolution,[status(thm)],[f42,f248]) ).
fof(f266,definition,
( sQ0_spl
<=> subset(inverse_image2(sK39_skl,empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( sQ0_spl
| ~ subset(inverse_image2(sK39_skl,empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,definition,
( sQ1_spl
<=> subset(empty_set,inverse_image2(sK39_skl,empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( sQ1_spl
| ~ subset(empty_set,inverse_image2(sK39_skl,empty_set)) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f265,f266,f269]) ).
fof(f286,plain,
( sQ0_spl
| member(sK0_skl(empty_set,inverse_image2(sK39_skl,empty_set)),inverse_image2(sK39_skl,empty_set)) ),
inference(resolution,[status(thm)],[f36,f268]) ).
fof(f604,plain,
( sQ1_spl
| member(sK0_skl(inverse_image2(sK39_skl,empty_set),empty_set),empty_set) ),
inference(resolution,[status(thm)],[f271,f36]) ).
fof(f607,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f57]) ).
fof(f608,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f607]) ).
fof(f656,plain,
( sQ0_spl
| member(sK25_skl(sK0_skl(empty_set,inverse_image2(sK39_skl,empty_set)),empty_set,sK39_skl),empty_set) ),
inference(resolution,[status(thm)],[f286,f192]) ).
fof(f658,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f656,f57]) ).
fof(f659,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f658]) ).
fof(f660,plain,
$false,
inference(sat_refutation,[status(thm)],[f272,f608,f659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n010.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 05:36:48 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 0.14/5.41 % Refutation found
% 0.14/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.45 % Elapsed time: 0.058732 seconds
% 0.14/5.45 % CPU time: 0.214806 seconds
% 0.14/5.45 % Total memory used: 79.884 MB
% 0.14/5.45 % Net memory used: 79.591 MB
%------------------------------------------------------------------------------