%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU255+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 : n011.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 02:19:55 PM UTC 2026
% Result : Theorem 0.17s 5.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 6 unt; 2 def)
% Number of atoms : 153 ( 11 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 176 ( 69 ~; 74 |; 19 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 73 ( 67 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
=> B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [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(f28,conjecture,
! [A,B] :
( relation(B)
=> ( antisymmetric(B)
=> antisymmetric(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( antisymmetric(B)
=> antisymmetric(relation_restriction(B,A)) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f48,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f49,plain,
! [A] :
( ! [B] : relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f57,plain,
! [A] :
( ( antisymmetric(A)
<=> ! [B,C] :
( B = C
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f58,plain,
! [A] :
( ( ( ? [B,C] :
( B != C
& in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
| antisymmetric(A) )
& ( ! [B,C] :
( B = C
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A) )
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [A] :
( ( ( ( sK1_skl(A) != sK2_skl(A)
& in(ordered_pair(sK2_skl(A),sK1_skl(A)),A)
& in(ordered_pair(sK1_skl(A),sK2_skl(A)),A) )
| antisymmetric(A) )
& ( ! [B,C] :
( B = C
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A) )
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(B,sK1_skl(A)),skolemize(C,sK2_skl(A))],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] :
( in(ordered_pair(sK1_skl(X0),sK2_skl(X0)),X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
! [X0] :
( in(ordered_pair(sK2_skl(X0),sK1_skl(X0)),X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f63,plain,
! [X0] :
( sK1_skl(X0) != sK2_skl(X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f79,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(f80,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)],[f79]) ).
fof(f81,plain,
! [C] :
( ( ! [A,B] :
( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| in(A,relation_restriction(C,B)) )
& ! [A,B] :
( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( in(X1,X0)
| ~ in(X1,relation_restriction(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f87,plain,
? [A,B] :
( ~ antisymmetric(relation_restriction(B,A))
& antisymmetric(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f88,plain,
? [B] :
( ? [A] : ~ antisymmetric(relation_restriction(B,A))
& antisymmetric(B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f87]) ).
fof(f89,plain,
( ~ antisymmetric(relation_restriction(sK8_skl,sK9_skl))
& antisymmetric(sK8_skl)
& relation(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(B,sK8_skl),skolemize(A,sK9_skl)],[f88]) ).
fof(f90,plain,
relation(sK8_skl),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
antisymmetric(sK8_skl),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f92,plain,
~ antisymmetric(relation_restriction(sK8_skl,sK9_skl)),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f124,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| antisymmetric(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f61,f82]) ).
fof(f126,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| antisymmetric(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f124,f50]) ).
fof(f137,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(relation_restriction(X0,X1)),sK1_skl(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| antisymmetric(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f62,f82]) ).
fof(f139,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(relation_restriction(X0,X1)),sK1_skl(relation_restriction(X0,X1))),X0)
| ~ relation(X0)
| antisymmetric(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f50]) ).
fof(f142,plain,
! [X0,X1] :
( sK1_skl(relation_restriction(X0,X1)) = sK2_skl(relation_restriction(X0,X1))
| ~ in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),X0)
| ~ antisymmetric(X0)
| ~ relation(X0)
| ~ relation(X0)
| antisymmetric(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f139,f60]) ).
fof(f145,plain,
! [X0,X1] :
( sK1_skl(relation_restriction(X0,X1)) = sK2_skl(relation_restriction(X0,X1))
| ~ in(ordered_pair(sK1_skl(relation_restriction(X0,X1)),sK2_skl(relation_restriction(X0,X1))),X0)
| ~ antisymmetric(X0)
| ~ relation(X0)
| antisymmetric(relation_restriction(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f142]) ).
fof(f146,plain,
! [X0,X1] :
( sK1_skl(relation_restriction(X0,X1)) = sK2_skl(relation_restriction(X0,X1))
| ~ antisymmetric(X0)
| ~ relation(X0)
| antisymmetric(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f126]) ).
fof(f148,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1))
| ~ antisymmetric(X0)
| ~ relation(X0)
| antisymmetric(relation_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f146,f63]) ).
fof(f149,plain,
! [X0,X1] :
( ~ relation(relation_restriction(X0,X1))
| ~ antisymmetric(X0)
| ~ relation(X0)
| antisymmetric(relation_restriction(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f148]) ).
fof(f150,plain,
! [X0,X1] :
( ~ antisymmetric(X0)
| ~ relation(X0)
| antisymmetric(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f50]) ).
fof(f151,plain,
( ~ antisymmetric(sK8_skl)
| ~ relation(sK8_skl) ),
inference(resolution,[status(thm)],[f150,f92]) ).
fof(f152,definition,
( sQ0_spl
<=> relation(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( sQ0_spl
| ~ relation(sK8_skl) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,definition,
( sQ1_spl
<=> antisymmetric(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( sQ1_spl
| ~ antisymmetric(sK8_skl) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f151,f152,f155]) ).
fof(f159,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f90]) ).
fof(f160,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f159]) ).
fof(f161,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f91]) ).
fof(f162,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f163,plain,
$false,
inference(sat_refutation,[status(thm)],[f158,f160,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU255+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.43 % Computer : n011.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Mon Sep 21 06:03:45 UTC 2026
% 0.17/5.43 % CPUTime :
% 0.17/5.44 % Drodi V4.1.1
% 0.17/5.48 % Refutation found
% 0.17/5.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/5.52 % Elapsed time: 0.068868 seconds
% 0.20/5.52 % CPU time: 0.149192 seconds
% 0.20/5.52 % Total memory used: 35.999 MB
% 0.20/5.52 % Net memory used: 35.967 MB
%------------------------------------------------------------------------------