%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU239+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 : n005.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 02:19:51 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 97 ( 14 unt; 14 def)
% Number of atoms : 262 ( 6 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 276 ( 111 ~; 110 |; 24 &)
% ( 20 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 15 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 62 ( 55 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f28,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f41,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f45,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f48,plain,
! [A] :
( ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f49,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) )
| is_reflexive_in(A,B) )
& ( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) )
| is_reflexive_in(A,B) )
& ! [B] :
( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f51,plain,
! [A] :
( ( ! [B] :
( ( ~ in(ordered_pair(sK0_skl(B,A),sK0_skl(B,A)),A)
& in(sK0_skl(B,A),B) )
| is_reflexive_in(A,B) )
& ! [B] :
( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X1)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0_skl(X1,X0),sK0_skl(X1,X0)),X0)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f58,plain,
! [A] :
( ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f59,plain,
! [A] :
( ( ( ~ is_reflexive_in(A,relation_field(A))
| reflexive(A) )
& ( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] :
( ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f64,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f74,plain,
? [A] :
( ( reflexive(A)
<~> ! [B] :
( in(ordered_pair(B,B),A)
| ~ in(B,relation_field(A)) ) )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f75,plain,
? [A] :
( ( ? [B] :
( ~ in(ordered_pair(B,B),A)
& in(B,relation_field(A)) )
| ~ reflexive(A) )
& ( ! [B] :
( in(ordered_pair(B,B),A)
| ~ in(B,relation_field(A)) )
| reflexive(A) )
& relation(A) ),
inference(NNF_transformation,[status(thm)],[f74]) ).
fof(f76,plain,
( ( ( ~ in(ordered_pair(sK3_skl,sK3_skl),sK2_skl)
& in(sK3_skl,relation_field(sK2_skl)) )
| ~ reflexive(sK2_skl) )
& ( ! [B] :
( in(ordered_pair(B,B),sK2_skl)
| ~ in(B,relation_field(sK2_skl)) )
| reflexive(sK2_skl) )
& relation(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f75]) ).
fof(f77,plain,
relation(sK2_skl),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0] :
( in(ordered_pair(X0,X0),sK2_skl)
| ~ in(X0,relation_field(sK2_skl))
| reflexive(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,plain,
( in(sK3_skl,relation_field(sK2_skl))
| ~ reflexive(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,plain,
( ~ in(ordered_pair(sK3_skl,sK3_skl),sK2_skl)
| ~ reflexive(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f84,plain,
empty(sK5_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f28]) ).
fof(f85,plain,
empty(sK5_skl),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
( function(sK6_skl)
& empty(sK6_skl)
& relation(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f29]) ).
fof(f87,plain,
relation(sK6_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
empty(sK6_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f101,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f102,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f109,definition,
( sQ0_spl
<=> reflexive(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f112,definition,
! [X0] :
( sQ1_spl
<=> ( in(ordered_pair(X0,X0),sK2_skl)
| ~ in(X0,relation_field(sK2_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f113,plain,
! [X0] :
( ~ sQ1_spl
| in(ordered_pair(X0,X0),sK2_skl)
| ~ in(X0,relation_field(sK2_skl)) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f78,f109,f112]) ).
fof(f116,definition,
( sQ2_spl
<=> in(sK3_skl,relation_field(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f117,plain,
( ~ sQ2_spl
| in(sK3_skl,relation_field(sK2_skl)) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f79,f109,f116]) ).
fof(f120,definition,
( sQ3_spl
<=> in(ordered_pair(sK3_skl,sK3_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( sQ3_spl
| ~ in(ordered_pair(sK3_skl,sK3_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,plain,
( ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f80,f109,f120]) ).
fof(f138,plain,
! [X0] :
( one_to_one(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f45,f41]) ).
fof(f139,plain,
( one_to_one(empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f64,f138]) ).
fof(f141,definition,
( sQ6_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( sQ6_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,definition,
( sQ7_spl
<=> one_to_one(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f139,f141,f144]) ).
fof(f148,plain,
( one_to_one(sK5_skl)
| ~ relation(sK5_skl) ),
inference(resolution,[status(thm)],[f85,f138]) ).
fof(f150,definition,
( sQ8_spl
<=> relation(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( sQ8_spl
| ~ relation(sK5_skl) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
( sQ9_spl
<=> one_to_one(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f148,f150,f153]) ).
fof(f157,plain,
( one_to_one(sK6_skl)
| ~ relation(sK6_skl) ),
inference(resolution,[status(thm)],[f88,f138]) ).
fof(f159,definition,
( sQ10_spl
<=> relation(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( sQ10_spl
| ~ relation(sK6_skl) ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,definition,
( sQ11_spl
<=> one_to_one(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f157,f159,f162]) ).
fof(f166,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f87]) ).
fof(f167,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f166]) ).
fof(f176,plain,
! [X0] :
( sQ3_spl
| ~ in(sK3_skl,X0)
| ~ is_reflexive_in(sK2_skl,X0)
| ~ relation(sK2_skl) ),
inference(resolution,[status(thm)],[f52,f122]) ).
fof(f179,definition,
( sQ12_spl
<=> relation(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ12_spl
| ~ relation(sK2_skl) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,definition,
! [X0] :
( sQ13_spl
<=> ( ~ in(sK3_skl,X0)
| ~ is_reflexive_in(sK2_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f183,plain,
! [X0] :
( ~ sQ13_spl
| ~ in(sK3_skl,X0)
| ~ is_reflexive_in(sK2_skl,X0) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( sQ3_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f176,f179,f182,f120]) ).
fof(f186,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f77]) ).
fof(f187,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f186]) ).
fof(f188,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ is_reflexive_in(sK2_skl,relation_field(sK2_skl)) ),
inference(resolution,[status(thm)],[f183,f117]) ).
fof(f189,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ reflexive(sK2_skl)
| ~ relation(sK2_skl) ),
inference(resolution,[status(thm)],[f188,f60]) ).
fof(f190,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f189,f179,f109,f182,f116]) ).
fof(f233,plain,
sK6_skl = empty_set,
inference(resolution,[status(thm)],[f102,f88]) ).
fof(f234,plain,
sK5_skl = empty_set,
inference(resolution,[status(thm)],[f102,f85]) ).
fof(f238,plain,
( sQ6_spl
| ~ relation(sK6_skl) ),
inference(backward_demodulation,[status(thm)],[f233,f143]) ).
fof(f241,plain,
( sQ6_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f238,f159,f141]) ).
fof(f244,plain,
( sQ8_spl
| ~ relation(sK6_skl) ),
inference(backward_demodulation,[status(thm)],[f247,f152]) ).
fof(f247,plain,
sK5_skl = sK6_skl,
inference(forward_demodulation,[status(thm)],[f233,f234]) ).
fof(f248,plain,
( sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f244,f159,f150]) ).
fof(f276,plain,
! [X0] :
( ~ sQ1_spl
| ~ in(sK0_skl(X0,sK2_skl),relation_field(sK2_skl))
| is_reflexive_in(sK2_skl,X0)
| ~ relation(sK2_skl) ),
inference(resolution,[status(thm)],[f54,f113]) ).
fof(f278,definition,
! [X0] :
( sQ18_spl
<=> ( ~ in(sK0_skl(X0,sK2_skl),relation_field(sK2_skl))
| is_reflexive_in(sK2_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f279,plain,
! [X0] :
( ~ sQ18_spl
| ~ in(sK0_skl(X0,sK2_skl),relation_field(sK2_skl))
| is_reflexive_in(sK2_skl,X0) ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,plain,
( ~ sQ1_spl
| sQ18_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f276,f179,f278,f112]) ).
fof(f290,plain,
( ~ sQ18_spl
| is_reflexive_in(sK2_skl,relation_field(sK2_skl))
| ~ relation(sK2_skl)
| is_reflexive_in(sK2_skl,relation_field(sK2_skl)) ),
inference(resolution,[status(thm)],[f279,f53]) ).
fof(f291,definition,
( sQ19_spl
<=> is_reflexive_in(sK2_skl,relation_field(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( ~ sQ19_spl
| is_reflexive_in(sK2_skl,relation_field(sK2_skl)) ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f290,f291,f179,f278]) ).
fof(f295,plain,
( ~ sQ19_spl
| reflexive(sK2_skl)
| ~ relation(sK2_skl) ),
inference(resolution,[status(thm)],[f292,f61]) ).
fof(f297,plain,
( ~ sQ19_spl
| sQ0_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f295,f179,f109,f291]) ).
fof(f299,plain,
$false,
inference(sat_refutation,[status(thm)],[f115,f119,f123,f147,f156,f165,f167,f185,f187,f190,f241,f248,f281,f294,f297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU239+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.40 % Computer : n005.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 21 06:02:03 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.41 % Drodi V4.1.1
% 0.11/0.43 % Refutation found
% 0.11/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.46 % Elapsed time: 0.058181 seconds
% 0.11/0.46 % CPU time: 0.147009 seconds
% 0.11/0.46 % Total memory used: 102.580 MB
% 0.11/0.46 % Net memory used: 102.465 MB
%------------------------------------------------------------------------------