%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU125+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 : 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 02:19:17 PM UTC 2026
% Result : Theorem 0.13s 0.49s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 6 unt; 2 def)
% Number of atoms : 133 ( 8 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 147 ( 53 ~; 58 |; 27 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 76 ( 69 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f23,plain,
! [A,B,C] :
( ( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
( ! [A,B,C] :
( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [A,B,C] :
( ( ( in(sK0_skl(C,B,A),B)
| in(sK0_skl(C,B,A),A)
| in(sK0_skl(C,B,A),C) )
& ( ( ~ in(sK0_skl(C,B,A),B)
& ~ in(sK0_skl(C,B,A),A) )
| ~ in(sK0_skl(C,B,A),C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f24]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f32,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f33,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
( ! [A,B] :
( ( ~ in(sK1_skl(B,A),B)
& in(sK1_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( in(sK1_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(sK1_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f63,plain,
? [A,B,C] :
( ~ subset(set_union2(A,C),B)
& subset(C,B)
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f64,plain,
( ~ subset(set_union2(sK4_skl,sK6_skl),sK5_skl)
& subset(sK6_skl,sK5_skl)
& subset(sK4_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl),skolemize(C,sK6_skl)],[f63]) ).
fof(f65,plain,
subset(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
subset(sK6_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
~ subset(set_union2(sK4_skl,sK6_skl),sK5_skl),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f26]) ).
fof(f115,plain,
! [X0] :
( in(X0,sK5_skl)
| ~ in(X0,sK6_skl) ),
inference(resolution,[status(thm)],[f36,f66]) ).
fof(f116,plain,
! [X0] :
( in(X0,sK5_skl)
| ~ in(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f36,f65]) ).
fof(f159,plain,
! [X0,X1,X2] :
( in(sK1_skl(X2,set_union2(X0,X1)),X1)
| in(sK1_skl(X2,set_union2(X0,X1)),X0)
| subset(set_union2(X0,X1),X2) ),
inference(resolution,[status(thm)],[f37,f68]) ).
fof(f172,plain,
! [X0] :
( subset(X0,sK5_skl)
| ~ in(sK1_skl(sK5_skl,X0),sK4_skl) ),
inference(resolution,[status(thm)],[f116,f38]) ).
fof(f813,plain,
( in(sK1_skl(sK5_skl,set_union2(sK4_skl,sK6_skl)),sK6_skl)
| in(sK1_skl(sK5_skl,set_union2(sK4_skl,sK6_skl)),sK4_skl) ),
inference(resolution,[status(thm)],[f159,f67]) ).
fof(f820,definition,
( sQ11_spl
<=> in(sK1_skl(sK5_skl,set_union2(sK4_skl,sK6_skl)),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f821,plain,
( ~ sQ11_spl
| in(sK1_skl(sK5_skl,set_union2(sK4_skl,sK6_skl)),sK4_skl) ),
inference(component_clause,[status(thm)],[f820]) ).
fof(f823,definition,
( sQ12_spl
<=> in(sK1_skl(sK5_skl,set_union2(sK4_skl,sK6_skl)),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f824,plain,
( ~ sQ12_spl
| in(sK1_skl(sK5_skl,set_union2(sK4_skl,sK6_skl)),sK6_skl) ),
inference(component_clause,[status(thm)],[f823]) ).
fof(f826,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f813,f820,f823]) ).
fof(f922,plain,
( ~ sQ11_spl
| subset(set_union2(sK4_skl,sK6_skl),sK5_skl) ),
inference(resolution,[status(thm)],[f821,f172]) ).
fof(f924,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f922,f67]) ).
fof(f925,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f924]) ).
fof(f926,plain,
( ~ sQ12_spl
| in(sK1_skl(sK5_skl,set_union2(sK4_skl,sK6_skl)),sK5_skl) ),
inference(resolution,[status(thm)],[f824,f115]) ).
fof(f1297,plain,
( ~ sQ12_spl
| subset(set_union2(sK4_skl,sK6_skl),sK5_skl) ),
inference(resolution,[status(thm)],[f926,f38]) ).
fof(f1299,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1297,f67]) ).
fof(f1300,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f1299]) ).
fof(f1301,plain,
$false,
inference(sat_refutation,[status(thm)],[f826,f925,f1300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU125+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % 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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:54:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.49 % Refutation found
% 0.13/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.53 % Elapsed time: 0.150445 seconds
% 0.13/0.53 % CPU time: 0.951472 seconds
% 0.13/0.53 % Total memory used: 116.506 MB
% 0.13/0.53 % Net memory used: 113.796 MB
%------------------------------------------------------------------------------