%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU130+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 : n003.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 02:19:18 PM UTC 2026
% Result : Theorem 0.13s 0.49s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 10 unt; 4 def)
% Number of atoms : 141 ( 19 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 158 ( 62 ~; 61 |; 24 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 72 ( 66 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f29,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)],[f28]) ).
fof(f30,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)],[f29]) ).
fof(f31,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_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,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,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_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f36,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_intersection2(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_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
( ! [A,B,C] :
( ( ( ( in(sK1_skl(C,B,A),B)
& in(sK1_skl(C,B,A),A) )
| in(sK1_skl(C,B,A),C) )
& ( ~ in(sK1_skl(C,B,A),B)
| ~ in(sK1_skl(C,B,A),A)
| ~ in(sK1_skl(C,B,A),C) ) )
| C = set_intersection2(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_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f36]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ in(sK1_skl(X0,X2,X1),X2)
| ~ in(sK1_skl(X0,X2,X1),X1)
| ~ in(sK1_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f42,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,X2,X1),X1)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f53,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f54,plain,
? [A,B] :
( set_intersection2(A,B) != A
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f55,plain,
( set_intersection2(sK4_skl,sK5_skl) != sK4_skl
& subset(sK4_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl)],[f54]) ).
fof(f56,plain,
subset(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
set_intersection2(sK4_skl,sK5_skl) != sK4_skl,
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f58,plain,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f908,plain,
! [X0] : subset(empty_set,X0),
inference(paramodulation,[status(thm)],[f58,f53]) ).
fof(f991,definition,
! [X0] :
( sQ64_spl
<=> ~ subset(X0,set_intersection2(sK4_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f992,plain,
! [X0] :
( ~ sQ64_spl
| ~ subset(X0,set_intersection2(sK4_skl,sK5_skl)) ),
inference(component_clause,[status(thm)],[f991]) ).
fof(f1106,plain,
( ~ in(sK1_skl(sK4_skl,sK5_skl,sK4_skl),sK5_skl)
| ~ in(sK1_skl(sK4_skl,sK5_skl,sK4_skl),sK4_skl)
| ~ in(sK1_skl(sK4_skl,sK5_skl,sK4_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f41,f57]) ).
fof(f1111,definition,
( sQ78_spl
<=> in(sK1_skl(sK4_skl,sK5_skl,sK4_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1112,plain,
( ~ sQ78_spl
| in(sK1_skl(sK4_skl,sK5_skl,sK4_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f1111]) ).
fof(f1113,plain,
( sQ78_spl
| ~ in(sK1_skl(sK4_skl,sK5_skl,sK4_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f1111]) ).
fof(f1114,definition,
( sQ79_spl
<=> in(sK1_skl(sK4_skl,sK5_skl,sK4_skl),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1116,plain,
( sQ79_spl
| ~ in(sK1_skl(sK4_skl,sK5_skl,sK4_skl),sK5_skl) ),
inference(component_clause,[status(thm)],[f1114]) ).
fof(f1117,plain,
( ~ sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f1106,f1111,f1114]) ).
fof(f1143,plain,
( sQ78_spl
| in(sK1_skl(sK4_skl,sK5_skl,sK4_skl),sK4_skl)
| sK4_skl = set_intersection2(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f1113,f42]) ).
fof(f1150,definition,
( sQ81_spl
<=> sK4_skl = set_intersection2(sK4_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1151,plain,
( ~ sQ81_spl
| sK4_skl = set_intersection2(sK4_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f1150]) ).
fof(f1159,plain,
( sQ78_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f1143,f1150,f1111]) ).
fof(f1160,plain,
( ~ sQ81_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1151,f57]) ).
fof(f1161,plain,
~ sQ81_spl,
inference(contradiction_clause,[status(thm)],[f1160]) ).
fof(f1169,plain,
! [X0] :
( sQ79_spl
| ~ in(sK1_skl(sK4_skl,sK5_skl,sK4_skl),X0)
| ~ subset(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f1116,f32]) ).
fof(f1177,plain,
( ~ sQ64_spl
| $false ),
inference(resolution,[status(thm)],[f992,f908]) ).
fof(f1182,plain,
~ sQ64_spl,
inference(contradiction_clause,[status(thm)],[f1177]) ).
fof(f1232,plain,
( ~ sQ78_spl
| sQ79_spl
| ~ subset(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f1169,f1112]) ).
fof(f1243,plain,
( ~ sQ78_spl
| sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1232,f56]) ).
fof(f1244,plain,
( ~ sQ78_spl
| sQ79_spl ),
inference(contradiction_clause,[status(thm)],[f1243]) ).
fof(f1245,plain,
$false,
inference(sat_refutation,[status(thm)],[f1117,f1159,f1161,f1182,f1244]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU130+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:53:15 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % 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
% 0.27/0.54 % Elapsed time: 0.173205 seconds
% 0.27/0.54 % CPU time: 0.968921 seconds
% 0.27/0.54 % Total memory used: 109.394 MB
% 0.27/0.54 % Net memory used: 107.610 MB
%------------------------------------------------------------------------------