%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET679+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 02:10:25 PM UTC 2026
% Result : Theorem 0.18s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 102 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 120 ( 53 ~; 40 |; 12 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 44 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,B)
<=> member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ~ member(B,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( not_equal(B,C)
<=> B != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,conjecture,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> not_equal(identity_relation_of(B),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ ! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> not_equal(identity_relation_of(B),empty_set) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f26,plain,
! [B] :
( ! [C] :
( ( member(C,B)
<=> member(ordered_pair(C,C),identity_relation_of(B)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f27,plain,
! [B] :
( ! [C] :
( ( ( ~ member(ordered_pair(C,C),identity_relation_of(B))
| member(C,B) )
& ( member(ordered_pair(C,C),identity_relation_of(B))
| ~ member(C,B) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [B] :
( ~ member(B,empty_set)
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f31,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f49,plain,
! [B] :
( ! [C] :
( ( not_equal(B,C)
<=> B != C )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f50,plain,
! [B] :
( ! [C] :
( ( ( B = C
| not_equal(B,C) )
& ( B != C
| ~ not_equal(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
! [X0,X1] :
( X0 = X1
| not_equal(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
! [B] :
( ( empty(B)
<=> ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f54,plain,
! [B] :
( ( ( ? [C] :
( member(C,B)
& ilf_type(C,set_type) )
| empty(B) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [B] :
( ( ( ( member(sK1_skl(B),B)
& ilf_type(sK1_skl(B),set_type) )
| empty(B) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B))],[f54]) ).
fof(f58,plain,
! [X0] :
( member(sK1_skl(X0),X0)
| empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f107,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f108,plain,
? [B] :
( ~ not_equal(identity_relation_of(B),empty_set)
& ilf_type(B,set_type)
& ~ empty(B) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f109,plain,
( ~ not_equal(identity_relation_of(sK9_skl),empty_set)
& ilf_type(sK9_skl,set_type)
& ~ empty(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(B,sK9_skl)],[f108]) ).
fof(f110,plain,
~ empty(sK9_skl),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f112,plain,
~ not_equal(identity_relation_of(sK9_skl),empty_set),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f118,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f28,f107]) ).
fof(f119,plain,
! [X0,X1] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f107]) ).
fof(f121,plain,
! [X0] : ~ member(X0,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[f31,f107]) ).
fof(f132,plain,
! [X0] :
( member(sK1_skl(X0),X0)
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f107]) ).
fof(f136,plain,
! [X0,X1] :
( X1 = X0
| not_equal(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f52,f107]) ).
fof(f137,plain,
! [X0,X1] :
( X0 = X1
| not_equal(X0,X1) ),
inference(resolution,[status(thm)],[f136,f107]) ).
fof(f138,plain,
identity_relation_of(sK9_skl) = empty_set,
inference(resolution,[status(thm)],[f137,f112]) ).
fof(f145,plain,
! [X0] :
( member(ordered_pair(X0,X0),empty_set)
| ~ member(X0,sK9_skl) ),
inference(paramodulation,[status(thm)],[f138,f119]) ).
fof(f146,plain,
! [X0] : ~ member(X0,sK9_skl),
inference(forward_subsumption_resolution,[status(thm)],[f145,f121]) ).
fof(f147,plain,
empty(sK9_skl),
inference(resolution,[status(thm)],[f146,f132]) ).
fof(f148,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f147,f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET679+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n017.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Sep 21 05:27:41 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.18/0.43 % Drodi V4.1.1
% 0.18/0.45 % Refutation found
% 0.18/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.53 % Elapsed time: 0.110182 seconds
% 0.18/0.53 % CPU time: 0.102628 seconds
% 0.18/0.53 % Total memory used: 2.578 MB
% 0.18/0.53 % Net memory used: 2.576 MB
%------------------------------------------------------------------------------