%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET879+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 : n007.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 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 4 unt; 3 def)
% Number of atoms : 113 ( 63 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 126 ( 52 ~; 52 |; 13 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( set_difference(singleton(A),B) = singleton(A)
<=> ~ in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<=> A != B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<=> A != B ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f10,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)],[f2]) ).
fof(f11,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)],[f10]) ).
fof(f12,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))],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f17,plain,
! [A,B] :
( ( in(A,B)
| set_difference(singleton(A),B) = singleton(A) )
& ( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
( ! [A,B] :
( in(A,B)
| set_difference(singleton(A),B) = singleton(A) )
& ! [A,B] :
( ~ in(A,B)
| set_difference(singleton(A),B) != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_difference(singleton(X0),X1) != singleton(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( in(X0,X1)
| set_difference(singleton(X0),X1) = singleton(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f25,plain,
? [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<~> A != B ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
? [A,B] :
( ( A = B
| set_difference(singleton(A),singleton(B)) != singleton(A) )
& ( A != B
| set_difference(singleton(A),singleton(B)) = singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
( ( sK3_skl = sK4_skl
| set_difference(singleton(sK3_skl),singleton(sK4_skl)) != singleton(sK3_skl) )
& ( sK3_skl != sK4_skl
| set_difference(singleton(sK3_skl),singleton(sK4_skl)) = singleton(sK3_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f26]) ).
fof(f28,plain,
( sK3_skl != sK4_skl
| set_difference(singleton(sK3_skl),singleton(sK4_skl)) = singleton(sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
( sK3_skl = sK4_skl
| set_difference(singleton(sK3_skl),singleton(sK4_skl)) != singleton(sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,definition,
( sQ0_spl
<=> set_difference(singleton(sK3_skl),singleton(sK4_skl)) = singleton(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f31,plain,
( ~ sQ0_spl
| set_difference(singleton(sK3_skl),singleton(sK4_skl)) = singleton(sK3_skl) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f32,plain,
( sQ0_spl
| set_difference(singleton(sK3_skl),singleton(sK4_skl)) != singleton(sK3_skl) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,definition,
( sQ1_spl
<=> sK3_skl = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f34,plain,
( ~ sQ1_spl
| sK3_skl = sK4_skl ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f28,f30,f33]) ).
fof(f37,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f30,f33]) ).
fof(f38,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f13]) ).
fof(f39,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f14]) ).
fof(f41,plain,
! [X0] : set_difference(singleton(X0),singleton(X0)) != singleton(X0),
inference(resolution,[status(thm)],[f39,f19]) ).
fof(f53,definition,
( sQ2_spl
<=> singleton(sK3_skl) = singleton(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ2_spl
| singleton(sK3_skl) != singleton(sK3_skl) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f63,plain,
! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[f38,f20]) ).
fof(f74,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| set_difference(singleton(sK3_skl),singleton(sK3_skl)) = singleton(sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f34,f31]) ).
fof(f75,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f41]) ).
fof(f76,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f75]) ).
fof(f77,plain,
( sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f55]) ).
fof(f78,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f77]) ).
fof(f81,plain,
( sQ0_spl
| sK3_skl = sK4_skl
| singleton(sK3_skl) != singleton(sK3_skl) ),
inference(paramodulation,[status(thm)],[f63,f32]) ).
fof(f84,plain,
( sQ0_spl
| sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f81,f53,f33,f30]) ).
fof(f86,plain,
$false,
inference(sat_refutation,[status(thm)],[f36,f37,f76,f78,f84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET879+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n007.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:40:21 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.53 % Elapsed time: 0.081197 seconds
% 0.17/0.53 % CPU time: 0.080756 seconds
% 0.17/0.53 % Total memory used: 5.042 MB
% 0.17/0.53 % Net memory used: 5.038 MB
%------------------------------------------------------------------------------