%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU245+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:19:53 PM UTC 2026
% Result : Theorem 0.17s 0.50s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 5 unt; 3 def)
% Number of atoms : 167 ( 15 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 188 ( 71 ~; 77 |; 29 &)
% ( 7 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 71 ( 60 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] :
( relation(A)
=> ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f73,plain,
! [A] :
( ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f74,plain,
! [X0,X1] :
( relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
? [A,B,C] :
( ( in(A,relation_restriction(C,B))
<~> ( in(A,cartesian_product2(B,B))
& in(A,C) ) )
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f76,plain,
? [A,B,C] :
( ( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| ~ in(A,relation_restriction(C,B)) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| in(A,relation_restriction(C,B)) )
& relation(C) ),
inference(NNF_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
? [C] :
( ? [A,B] :
( ( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| ~ in(A,relation_restriction(C,B)) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| in(A,relation_restriction(C,B)) ) )
& relation(C) ),
inference(miniscoping,[status(thm)],[f76]) ).
fof(f78,plain,
( ( ~ in(sK7_skl,cartesian_product2(sK8_skl,sK8_skl))
| ~ in(sK7_skl,sK6_skl)
| ~ in(sK7_skl,relation_restriction(sK6_skl,sK8_skl)) )
& ( ( in(sK7_skl,cartesian_product2(sK8_skl,sK8_skl))
& in(sK7_skl,sK6_skl) )
| in(sK7_skl,relation_restriction(sK6_skl,sK8_skl)) )
& relation(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl]),skolemize(C,sK6_skl),skolemize(A,sK7_skl),skolemize(B,sK8_skl)],[f77]) ).
fof(f79,plain,
relation(sK6_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,plain,
( in(sK7_skl,sK6_skl)
| in(sK7_skl,relation_restriction(sK6_skl,sK8_skl)) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f81,plain,
( in(sK7_skl,cartesian_product2(sK8_skl,sK8_skl))
| in(sK7_skl,relation_restriction(sK6_skl,sK8_skl)) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f82,plain,
( ~ in(sK7_skl,cartesian_product2(sK8_skl,sK8_skl))
| ~ in(sK7_skl,sK6_skl)
| ~ in(sK7_skl,relation_restriction(sK6_skl,sK8_skl)) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f83,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)],[f27]) ).
fof(f84,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)],[f83]) ).
fof(f85,plain,
( ! [A,B,C] :
( ( ( ( in(sK9_skl(C,B,A),B)
& in(sK9_skl(C,B,A),A) )
| in(sK9_skl(C,B,A),C) )
& ( ~ in(sK9_skl(C,B,A),B)
| ~ in(sK9_skl(C,B,A),A)
| ~ in(sK9_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,[sK9_skl]),skolemize(D,sK9_skl(C,B,A))],[f84]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f92,definition,
( sQ0_spl
<=> in(sK7_skl,relation_restriction(sK6_skl,sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f93,plain,
( ~ sQ0_spl
| in(sK7_skl,relation_restriction(sK6_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f94,plain,
( sQ0_spl
| ~ in(sK7_skl,relation_restriction(sK6_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,definition,
( sQ1_spl
<=> in(sK7_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ1_spl
| in(sK7_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f97,plain,
( sQ1_spl
| ~ in(sK7_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f80,f92,f95]) ).
fof(f99,definition,
( sQ2_spl
<=> in(sK7_skl,cartesian_product2(sK8_skl,sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ2_spl
| in(sK7_skl,cartesian_product2(sK8_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f101,plain,
( sQ2_spl
| ~ in(sK7_skl,cartesian_product2(sK8_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f92,f99]) ).
fof(f103,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f82,f92,f95,f99]) ).
fof(f105,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f86]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f88]) ).
fof(f110,plain,
! [X0] : relation_restriction(sK6_skl,X0) = set_intersection2(sK6_skl,cartesian_product2(X0,X0)),
inference(resolution,[status(thm)],[f74,f79]) ).
fof(f167,plain,
! [X0] :
( sQ1_spl
| ~ in(sK7_skl,set_intersection2(sK6_skl,X0)) ),
inference(resolution,[status(thm)],[f105,f97]) ).
fof(f173,plain,
! [X0] :
( sQ1_spl
| ~ in(sK7_skl,relation_restriction(sK6_skl,X0)) ),
inference(paramodulation,[status(thm)],[f110,f167]) ).
fof(f178,plain,
( ~ sQ0_spl
| sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f93,f173]) ).
fof(f179,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f285,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(sK7_skl,X0)
| in(sK7_skl,set_intersection2(X0,cartesian_product2(sK8_skl,sK8_skl))) ),
inference(resolution,[status(thm)],[f107,f100]) ).
fof(f339,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| in(sK7_skl,set_intersection2(sK6_skl,cartesian_product2(sK8_skl,sK8_skl))) ),
inference(resolution,[status(thm)],[f285,f96]) ).
fof(f342,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| in(sK7_skl,relation_restriction(sK6_skl,sK8_skl)) ),
inference(forward_demodulation,[status(thm)],[f110,f339]) ).
fof(f343,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f342,f94]) ).
fof(f344,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f352,plain,
! [X0] :
( sQ2_spl
| ~ in(sK7_skl,set_intersection2(cartesian_product2(sK8_skl,sK8_skl),X0)) ),
inference(resolution,[status(thm)],[f101,f105]) ).
fof(f370,plain,
! [X0] :
( sQ2_spl
| ~ in(sK7_skl,set_intersection2(X0,cartesian_product2(sK8_skl,sK8_skl))) ),
inference(paramodulation,[status(thm)],[f60,f352]) ).
fof(f421,plain,
( sQ2_spl
| ~ in(sK7_skl,relation_restriction(sK6_skl,sK8_skl)) ),
inference(paramodulation,[status(thm)],[f110,f370]) ).
fof(f425,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f421,f92,f99]) ).
fof(f426,plain,
$false,
inference(sat_refutation,[status(thm)],[f98,f102,f103,f179,f344,f425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU245+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n019.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 06:03:05 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.50 % Refutation found
% 0.17/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.29/0.55 % Elapsed time: 0.100014 seconds
% 0.29/0.55 % CPU time: 0.379663 seconds
% 0.29/0.55 % Total memory used: 105.856 MB
% 0.29/0.55 % Net memory used: 105.401 MB
%------------------------------------------------------------------------------