%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU134+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 02:19:19 PM UTC 2026
% Result : Theorem 0.14s 0.57s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 1 unt; 2 def)
% Number of atoms : 58 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 56 ( 23 ~; 23 |; 4 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,conjecture,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
? [A,B] :
( set_difference(A,B) = empty_set
<~> subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f36,plain,
? [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) != empty_set )
& ( subset(A,B)
| set_difference(A,B) = empty_set ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
( ( ~ subset(sK2_skl,sK3_skl)
| set_difference(sK2_skl,sK3_skl) != empty_set )
& ( subset(sK2_skl,sK3_skl)
| set_difference(sK2_skl,sK3_skl) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f36]) ).
fof(f38,plain,
( subset(sK2_skl,sK3_skl)
| set_difference(sK2_skl,sK3_skl) = empty_set ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
( ~ subset(sK2_skl,sK3_skl)
| set_difference(sK2_skl,sK3_skl) != empty_set ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f41,plain,
( ! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ! [A,B] :
( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,definition,
( sQ0_spl
<=> set_difference(sK2_skl,sK3_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( sQ0_spl
| set_difference(sK2_skl,sK3_skl) != empty_set ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,definition,
( sQ1_spl
<=> subset(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f48,plain,
( ~ sQ1_spl
| subset(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f49,plain,
( sQ1_spl
| ~ subset(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f44,f47]) ).
fof(f51,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f44,f47]) ).
fof(f54,plain,
( ~ sQ1_spl
| set_difference(sK2_skl,sK3_skl) = empty_set ),
inference(resolution,[status(thm)],[f43,f48]) ).
fof(f57,plain,
( ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f46]) ).
fof(f58,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f57]) ).
fof(f63,plain,
( sQ1_spl
| set_difference(sK2_skl,sK3_skl) != empty_set ),
inference(resolution,[status(thm)],[f49,f42]) ).
fof(f64,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f44,f47]) ).
fof(f65,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f51,f58,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU134+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.53 % Computer : n008.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.53 % CPULimit : 300
% 0.10/0.53 % WCLimit : 300
% 0.10/0.53 % DateTime : Mon Sep 21 05:52:54 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.55 % Drodi V4.1.1
% 0.14/0.57 % Refutation found
% 0.14/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.58 % Elapsed time: 0.043082 seconds
% 0.14/0.58 % CPU time: 0.123843 seconds
% 0.14/0.58 % Total memory used: 69.693 MB
% 0.14/0.58 % Net memory used: 69.421 MB
%------------------------------------------------------------------------------