%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU112+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 02:19:14 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 13 unt; 2 def)
% Number of atoms : 48 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 18 ~; 14 |; 1 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,conjecture,
! [A,B] : subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ ! [A,B] : subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f39,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f128,plain,
! [A,B] :
( subset(finite_subsets(A),finite_subsets(B))
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f129,plain,
! [X0,X1] :
( subset(finite_subsets(X0),finite_subsets(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
? [A,B] : ~ subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f131,plain,
~ subset(set_union2(finite_subsets(sK10_skl),finite_subsets(sK11_skl)),finite_subsets(set_union2(sK10_skl,sK11_skl))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl]),skolemize(A,sK10_skl),skolemize(B,sK11_skl)],[f130]) ).
fof(f132,plain,
~ subset(set_union2(finite_subsets(sK10_skl),finite_subsets(sK11_skl)),finite_subsets(set_union2(sK10_skl,sK11_skl))),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f150,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f154,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f155,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f163,plain,
! [X0,X1] : subset(X0,set_union2(X1,X0)),
inference(paramodulation,[status(thm)],[f56,f150]) ).
fof(f180,plain,
( ~ subset(finite_subsets(sK11_skl),finite_subsets(set_union2(sK10_skl,sK11_skl)))
| ~ subset(finite_subsets(sK10_skl),finite_subsets(set_union2(sK10_skl,sK11_skl))) ),
inference(resolution,[status(thm)],[f155,f132]) ).
fof(f184,definition,
( sQ0_spl
<=> subset(finite_subsets(sK10_skl),finite_subsets(set_union2(sK10_skl,sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( sQ0_spl
| ~ subset(finite_subsets(sK10_skl),finite_subsets(set_union2(sK10_skl,sK11_skl))) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,definition,
( sQ1_spl
<=> subset(finite_subsets(sK11_skl),finite_subsets(set_union2(sK10_skl,sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( sQ1_spl
| ~ subset(finite_subsets(sK11_skl),finite_subsets(set_union2(sK10_skl,sK11_skl))) ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f180,f184,f187]) ).
fof(f196,plain,
( sQ0_spl
| ~ subset(sK10_skl,set_union2(sK10_skl,sK11_skl)) ),
inference(resolution,[status(thm)],[f186,f129]) ).
fof(f199,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f150]) ).
fof(f200,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f199]) ).
fof(f201,plain,
( sQ1_spl
| ~ subset(sK11_skl,set_union2(sK10_skl,sK11_skl)) ),
inference(resolution,[status(thm)],[f189,f129]) ).
fof(f204,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f163]) ).
fof(f205,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f206,plain,
$false,
inference(sat_refutation,[status(thm)],[f190,f200,f205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU112+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:50:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.063276 seconds
% 0.09/0.44 % CPU time: 0.154283 seconds
% 0.09/0.44 % Total memory used: 103.243 MB
% 0.09/0.44 % Net memory used: 103.208 MB
%------------------------------------------------------------------------------