%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU162+3 : 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 02:19:28 PM UTC 2026
% Result : Theorem 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 1 unt; 2 def)
% Number of atoms : 84 ( 19 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 82 ( 36 ~; 33 |; 5 &)
% ( 5 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f20,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
? [A,B] :
( set_difference(A,singleton(B)) = A
<~> ~ in(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
? [A,B] :
( ( in(B,A)
| set_difference(A,singleton(B)) != A )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) = A ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
( ( in(sK3_skl,sK2_skl)
| set_difference(sK2_skl,singleton(sK3_skl)) != sK2_skl )
& ( ~ in(sK3_skl,sK2_skl)
| set_difference(sK2_skl,singleton(sK3_skl)) = sK2_skl ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f23]) ).
fof(f25,plain,
( ~ in(sK3_skl,sK2_skl)
| set_difference(sK2_skl,singleton(sK3_skl)) = sK2_skl ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
( in(sK3_skl,sK2_skl)
| set_difference(sK2_skl,singleton(sK3_skl)) != sK2_skl ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f27,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
( ! [A,B] :
( set_difference(A,B) != A
| disjoint(A,B) )
& ! [A,B] :
( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,definition,
( sQ0_spl
<=> set_difference(sK2_skl,singleton(sK3_skl)) = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f32,plain,
( ~ sQ0_spl
| set_difference(sK2_skl,singleton(sK3_skl)) = sK2_skl ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f33,plain,
( sQ0_spl
| set_difference(sK2_skl,singleton(sK3_skl)) != sK2_skl ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,definition,
( sQ1_spl
<=> in(sK3_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( sQ1_spl
| ~ in(sK3_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f25,f31,f34]) ).
fof(f38,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f26,f31,f34]) ).
fof(f39,plain,
( sQ0_spl
| ~ disjoint(sK2_skl,singleton(sK3_skl)) ),
inference(resolution,[status(thm)],[f29,f33]) ).
fof(f42,plain,
! [X0,X1] :
( in(X1,X0)
| disjoint(X0,singleton(X1)) ),
inference(resolution,[status(thm)],[f21,f15]) ).
fof(f44,plain,
( sQ0_spl
| in(sK3_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f42,f39]) ).
fof(f46,plain,
( sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f36]) ).
fof(f47,plain,
( sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f46]) ).
fof(f49,plain,
( ~ sQ0_spl
| disjoint(sK2_skl,singleton(sK3_skl)) ),
inference(resolution,[status(thm)],[f32,f30]) ).
fof(f60,plain,
( ~ sQ0_spl
| disjoint(singleton(sK3_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f49,f21]) ).
fof(f61,plain,
( ~ sQ0_spl
| ~ in(sK3_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f60,f13]) ).
fof(f63,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f61,f34,f31]) ).
fof(f64,plain,
$false,
inference(sat_refutation,[status(thm)],[f37,f38,f47,f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU162+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n015.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 05:57:20 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 0.09/0.37 % Refutation found
% 0.09/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.042567 seconds
% 0.13/0.39 % CPU time: 0.117432 seconds
% 0.13/0.39 % Total memory used: 59.868 MB
% 0.13/0.39 % Net memory used: 59.524 MB
%------------------------------------------------------------------------------