%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 02:10:53 PM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 6 unt; 2 def)
% Number of atoms : 96 ( 47 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 112 ( 46 ~; 41 |; 18 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f12,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f14,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f19,plain,
! [A,B,C] :
( ( ( A != B
& ~ in(B,C) )
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) )
& ( ( ( A = B
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
( ! [A,B,C] :
( ( A != B
& ~ in(B,C) )
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) )
& ! [A,B,C] :
( ( ( A = B
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f29,plain,
? [A,B] :
( set_difference(unordered_pair(A,B),singleton(B)) != singleton(A)
& A != B ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f30,plain,
( set_difference(unordered_pair(sK3_skl,sK4_skl),singleton(sK4_skl)) != singleton(sK3_skl)
& sK3_skl != sK4_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f29]) ).
fof(f31,plain,
sK3_skl != sK4_skl,
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
set_difference(unordered_pair(sK3_skl,sK4_skl),singleton(sK4_skl)) != singleton(sK3_skl),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f15]) ).
fof(f34,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f16]) ).
fof(f59,plain,
( ~ in(sK4_skl,singleton(sK4_skl))
| in(sK3_skl,singleton(sK4_skl)) ),
inference(resolution,[status(thm)],[f23,f32]) ).
fof(f67,definition,
( sQ0_spl
<=> in(sK3_skl,singleton(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ0_spl
| in(sK3_skl,singleton(sK4_skl)) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,definition,
( sQ1_spl
<=> in(sK4_skl,singleton(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( sQ1_spl
| ~ in(sK4_skl,singleton(sK4_skl)) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f67,f70]) ).
fof(f74,plain,
( ~ sQ0_spl
| sK3_skl = sK4_skl ),
inference(resolution,[status(thm)],[f68,f33]) ).
fof(f75,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f31]) ).
fof(f76,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f75]) ).
fof(f77,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f34]) ).
fof(f78,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f77]) ).
fof(f79,plain,
$false,
inference(sat_refutation,[status(thm)],[f73,f76,f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:45:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.071525 seconds
% 0.14/0.45 % CPU time: 0.095051 seconds
% 0.14/0.45 % Total memory used: 9.554 MB
% 0.14/0.45 % Net memory used: 9.541 MB
%------------------------------------------------------------------------------