%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET016+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 02:08:52 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 8 unt; 2 def)
% Number of atoms : 125 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 129 ( 51 ~; 48 |; 20 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 87 ( 77 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,A,B] :
( member(X,unordered_pair(A,B))
<=> ( X = B
| X = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,U,V] :
( equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))
=> A = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,U,V] :
( equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))
=> A = U ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,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)],[f14]) ).
fof(f16,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)],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,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(f22,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)],[f21]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f46,plain,
! [X,A] :
( ( X != A
| member(X,singleton(A)) )
& ( X = A
| ~ member(X,singleton(A)) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f47,plain,
( ! [X,A] :
( X != A
| member(X,singleton(A)) )
& ! [X,A] :
( X = A
| ~ member(X,singleton(A)) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( X0 != X1
| member(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X,A,B] :
( ( ( X != B
& X != A )
| member(X,unordered_pair(A,B)) )
& ( X = B
| X = A
| ~ member(X,unordered_pair(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f51,plain,
( ! [X,A,B] :
( ( X != B
& X != A )
| member(X,unordered_pair(A,B)) )
& ! [X,A,B] :
( X = B
| X = A
| ~ member(X,unordered_pair(A,B)) ) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( X0 != X1
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f68,plain,
? [A,B,U,V] :
( A != U
& equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V))) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
? [A,U] :
( A != U
& ? [B,V] : equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V))) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f70,plain,
( sK3_skl != sK4_skl
& equal_set(unordered_pair(singleton(sK3_skl),unordered_pair(sK3_skl,sK5_skl)),unordered_pair(singleton(sK4_skl),unordered_pair(sK4_skl,sK6_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK3_skl),skolemize(U,sK4_skl),skolemize(B,sK5_skl),skolemize(V,sK6_skl)],[f69]) ).
fof(f71,plain,
equal_set(unordered_pair(singleton(sK3_skl),unordered_pair(sK3_skl,sK5_skl)),unordered_pair(singleton(sK4_skl),unordered_pair(sK4_skl,sK6_skl))),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
sK3_skl != sK4_skl,
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
! [X0] : member(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f49]) ).
fof(f74,plain,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ equal_set(X2,X1)
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f18,f24]) ).
fof(f81,plain,
! [X0] :
( member(X0,unordered_pair(singleton(sK3_skl),unordered_pair(sK3_skl,sK5_skl)))
| ~ member(X0,unordered_pair(singleton(sK4_skl),unordered_pair(sK4_skl,sK6_skl))) ),
inference(resolution,[status(thm)],[f79,f71]) ).
fof(f94,plain,
member(singleton(sK4_skl),unordered_pair(singleton(sK3_skl),unordered_pair(sK3_skl,sK5_skl))),
inference(resolution,[status(thm)],[f81,f74]) ).
fof(f95,plain,
( singleton(sK4_skl) = unordered_pair(sK3_skl,sK5_skl)
| singleton(sK4_skl) = singleton(sK3_skl) ),
inference(resolution,[status(thm)],[f94,f52]) ).
fof(f96,definition,
( sQ0_spl
<=> singleton(sK4_skl) = singleton(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ0_spl
| singleton(sK4_skl) = singleton(sK3_skl) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,definition,
( sQ1_spl
<=> singleton(sK4_skl) = unordered_pair(sK3_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ1_spl
| singleton(sK4_skl) = unordered_pair(sK3_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f95,f96,f99]) ).
fof(f107,plain,
( ~ sQ0_spl
| member(sK4_skl,singleton(sK3_skl)) ),
inference(paramodulation,[status(thm)],[f97,f73]) ).
fof(f109,plain,
( ~ sQ0_spl
| sK4_skl = sK3_skl ),
inference(resolution,[status(thm)],[f107,f48]) ).
fof(f110,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f72]) ).
fof(f111,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f110]) ).
fof(f114,plain,
( ~ sQ1_spl
| member(sK3_skl,singleton(sK4_skl)) ),
inference(paramodulation,[status(thm)],[f100,f74]) ).
fof(f118,plain,
( ~ sQ1_spl
| sK3_skl = sK4_skl ),
inference(resolution,[status(thm)],[f114,f48]) ).
fof(f119,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f72]) ).
fof(f120,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f119]) ).
fof(f121,plain,
$false,
inference(sat_refutation,[status(thm)],[f102,f111,f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:45:16 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.044667 seconds
% 0.14/0.41 % CPU time: 0.125279 seconds
% 0.14/0.41 % Total memory used: 53.244 MB
% 0.14/0.41 % Net memory used: 53.082 MB
%------------------------------------------------------------------------------