%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU008+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:19:04 PM UTC 2026
% Result : Theorem 0.13s 0.51s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 13 unt; 2 def)
% Number of atoms : 217 ( 61 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 268 ( 106 ~; 104 |; 43 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 108 ( 98 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
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(f7,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,set_intersection2(relation_dom(C),A))
=> apply(C,B) = apply(relation_composition(identity_relation(A),C),B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,set_intersection2(relation_dom(C),A))
=> apply(C,B) = apply(relation_composition(identity_relation(A),C),B) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f50,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(f51,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)],[f50]) ).
fof(f52,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_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,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f51]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f61,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f77,plain,
( ! [A] : function(identity_relation(A))
& ! [A] : relation(identity_relation(A)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f79,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f119,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f120,plain,
! [B] :
( ! [C] :
( ! [A] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B)) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f121,plain,
! [X0,X1,X2] :
( apply(relation_composition(X0,X1),X2) = apply(X1,apply(X0,X2))
| ~ in(X2,relation_dom(X0))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f125,plain,
! [A,B] :
( ( B = identity_relation(A)
<=> ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A ) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f126,plain,
! [A,B] :
( ( ( ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [B] :
( ( ! [A] :
( ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ! [A] :
( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f126]) ).
fof(f128,plain,
! [B] :
( ( ! [A] :
( ( apply(B,sK10_skl(A,B)) != sK10_skl(A,B)
& in(sK10_skl(A,B),A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ! [A] :
( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(C,sK10_skl(A,B))],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| X0 != identity_relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [X0,X1,X2] :
( apply(X0,X2) = X2
| ~ in(X2,X1)
| X0 != identity_relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f133,plain,
? [A,B,C] :
( apply(C,B) != apply(relation_composition(identity_relation(A),C),B)
& in(B,set_intersection2(relation_dom(C),A))
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f134,plain,
? [C] :
( ? [A,B] :
( apply(C,B) != apply(relation_composition(identity_relation(A),C),B)
& in(B,set_intersection2(relation_dom(C),A)) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f133]) ).
fof(f135,plain,
( apply(sK11_skl,sK13_skl) != apply(relation_composition(identity_relation(sK12_skl),sK11_skl),sK13_skl)
& in(sK13_skl,set_intersection2(relation_dom(sK11_skl),sK12_skl))
& function(sK11_skl)
& relation(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl]),skolemize(C,sK11_skl),skolemize(A,sK12_skl),skolemize(B,sK13_skl)],[f134]) ).
fof(f136,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
function(sK11_skl),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f138,plain,
in(sK13_skl,set_intersection2(relation_dom(sK11_skl),sK12_skl)),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f139,plain,
apply(sK11_skl,sK13_skl) != apply(relation_composition(identity_relation(sK12_skl),sK11_skl),sK13_skl),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f159,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f54]) ).
fof(f161,plain,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f129]) ).
fof(f162,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f177,plain,
in(sK13_skl,sK12_skl),
inference(resolution,[status(thm)],[f159,f138]) ).
fof(f272,plain,
! [X0,X1] :
( apply(relation_composition(X0,sK11_skl),X1) = apply(sK11_skl,apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ function(sK11_skl)
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f121,f136]) ).
fof(f303,definition,
! [X0,X1] :
( sQ8_spl
<=> ( apply(relation_composition(X0,sK11_skl),X1) = apply(sK11_skl,apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f304,plain,
! [X0,X1] :
( ~ sQ8_spl
| apply(relation_composition(X0,sK11_skl),X1) = apply(sK11_skl,apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f306,definition,
( sQ9_spl
<=> function(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( sQ9_spl
| ~ function(sK11_skl) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,plain,
( ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f272,f303,f306]) ).
fof(f334,plain,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f61]) ).
fof(f335,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(resolution,[status(thm)],[f334,f79]) ).
fof(f337,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0)
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f61]) ).
fof(f338,plain,
! [X0,X1] :
( apply(identity_relation(X1),X0) = X0
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f337,f79]) ).
fof(f392,plain,
! [X0,X1] :
( ~ sQ8_spl
| apply(relation_composition(identity_relation(X0),sK11_skl),X1) = apply(sK11_skl,apply(identity_relation(X0),X1))
| ~ in(X1,relation_dom(identity_relation(X0)))
| ~ function(identity_relation(X0)) ),
inference(resolution,[status(thm)],[f304,f61]) ).
fof(f411,plain,
! [X0,X1] :
( ~ sQ8_spl
| apply(relation_composition(identity_relation(X0),sK11_skl),X1) = apply(sK11_skl,apply(identity_relation(X0),X1))
| ~ in(X1,X0)
| ~ function(identity_relation(X0)) ),
inference(forward_demodulation,[status(thm)],[f335,f392]) ).
fof(f412,plain,
! [X0,X1] :
( ~ sQ8_spl
| apply(relation_composition(identity_relation(X1),sK11_skl),X0) = apply(sK11_skl,apply(identity_relation(X1),X0))
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f411,f79]) ).
fof(f419,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f137]) ).
fof(f420,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f419]) ).
fof(f423,plain,
( ~ sQ8_spl
| apply(relation_composition(identity_relation(sK12_skl),sK11_skl),sK13_skl) = apply(sK11_skl,apply(identity_relation(sK12_skl),sK13_skl)) ),
inference(resolution,[status(thm)],[f412,f177]) ).
fof(f1240,plain,
apply(identity_relation(sK12_skl),sK13_skl) = sK13_skl,
inference(resolution,[status(thm)],[f338,f177]) ).
fof(f1244,plain,
( ~ sQ8_spl
| apply(relation_composition(identity_relation(sK12_skl),sK11_skl),sK13_skl) = apply(sK11_skl,sK13_skl) ),
inference(backward_demodulation,[status(thm)],[f1240,f423]) ).
fof(f1245,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1244,f139]) ).
fof(f1246,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f1245]) ).
fof(f1247,plain,
$false,
inference(sat_refutation,[status(thm)],[f309,f420,f1246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU008+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:46:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.13/0.51 % Refutation found
% 0.13/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.50/0.55 % Elapsed time: 0.165603 seconds
% 0.50/0.55 % CPU time: 0.983650 seconds
% 0.50/0.55 % Total memory used: 116.882 MB
% 0.50/0.55 % Net memory used: 115.394 MB
%------------------------------------------------------------------------------