%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU180+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 : n007.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 02:19:33 PM UTC 2026
% Result : Theorem 0.25s 0.52s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 5 unt; 6 def)
% Number of atoms : 265 ( 32 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 314 ( 121 ~; 128 |; 41 &)
% ( 16 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 153 ( 129 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f38,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f39,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,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_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f43,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_union2(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_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,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_union2(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_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f43]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f51,plain,
! [A] :
( ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f54,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK2_skl(B,A),sK3_skl(B,A)),A)
| in(sK2_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK2_skl(B,A),D),A)
| ~ in(sK2_skl(B,A),B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(C,sK1_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f53]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f59,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f60,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK6_skl(B,A),sK5_skl(B,A)),A)
| in(sK5_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK5_skl(B,A)),A)
| ~ in(sK5_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK4_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(D,sK4_skl(C,B,A)),skolemize(C,sK5_skl(B,A)),skolemize(D,sK6_skl(B,A))],[f61]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f68,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f69,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f98,plain,
? [A,B,C] :
( ( ~ in(B,relation_field(C))
| ~ in(A,relation_field(C)) )
& in(ordered_pair(A,B),C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f99,plain,
? [C] :
( ? [A,B] :
( ( ~ in(B,relation_field(C))
| ~ in(A,relation_field(C)) )
& in(ordered_pair(A,B),C) )
& relation(C) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f100,plain,
( ( ~ in(sK13_skl,relation_field(sK11_skl))
| ~ in(sK12_skl,relation_field(sK11_skl)) )
& in(ordered_pair(sK12_skl,sK13_skl),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)],[f99]) ).
fof(f101,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
in(ordered_pair(sK12_skl,sK13_skl),sK11_skl),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f103,plain,
( ~ in(sK13_skl,relation_field(sK11_skl))
| ~ in(sK12_skl,relation_field(sK11_skl)) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f112,definition,
( sQ0_spl
<=> in(sK12_skl,relation_field(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( sQ0_spl
| ~ in(sK12_skl,relation_field(sK11_skl)) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,definition,
( sQ1_spl
<=> in(sK13_skl,relation_field(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f117,plain,
( sQ1_spl
| ~ in(sK13_skl,relation_field(sK11_skl)) ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f103,f112,f115]) ).
fof(f119,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f45]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f46]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f47]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f56]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f64]) ).
fof(f128,plain,
relation_field(sK11_skl) = set_union2(relation_dom(sK11_skl),relation_rng(sK11_skl)),
inference(resolution,[status(thm)],[f69,f101]) ).
fof(f206,plain,
! [X0] :
( sQ0_spl
| in(sK12_skl,X0)
| ~ in(sK12_skl,set_union2(X0,relation_field(sK11_skl))) ),
inference(resolution,[status(thm)],[f119,f114]) ).
fof(f211,plain,
! [X0] :
( sQ0_spl
| ~ in(X0,sK12_skl)
| ~ in(sK12_skl,set_union2(X0,relation_field(sK11_skl))) ),
inference(resolution,[status(thm)],[f206,f39]) ).
fof(f499,plain,
( sQ0_spl
| ~ in(sK12_skl,set_union2(sK12_skl,relation_field(sK11_skl)))
| ~ in(sK12_skl,set_union2(sK12_skl,relation_field(sK11_skl))) ),
inference(resolution,[status(thm)],[f211,f206]) ).
fof(f503,definition,
( sQ25_spl
<=> in(sK12_skl,set_union2(sK12_skl,relation_field(sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ25_spl
| ~ in(sK12_skl,set_union2(sK12_skl,relation_field(sK11_skl))) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,plain,
( sQ0_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f499,f503,f112]) ).
fof(f536,definition,
( sQ26_spl
<=> relation(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f538,plain,
( sQ26_spl
| ~ relation(sK11_skl) ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f543,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f538,f101]) ).
fof(f544,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f557,plain,
( in(sK12_skl,relation_dom(sK11_skl))
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f123,f102]) ).
fof(f559,definition,
( sQ28_spl
<=> in(sK12_skl,relation_dom(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( ~ sQ28_spl
| in(sK12_skl,relation_dom(sK11_skl)) ),
inference(component_clause,[status(thm)],[f559]) ).
fof(f562,plain,
( sQ28_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f557,f536,f559]) ).
fof(f572,plain,
! [X0] :
( ~ sQ28_spl
| in(sK12_skl,set_union2(relation_dom(sK11_skl),X0)) ),
inference(resolution,[status(thm)],[f560,f120]) ).
fof(f625,plain,
( ~ sQ28_spl
| in(sK12_skl,relation_field(sK11_skl)) ),
inference(paramodulation,[status(thm)],[f128,f572]) ).
fof(f649,plain,
! [X0] :
( ~ sQ28_spl
| in(sK12_skl,set_union2(X0,relation_field(sK11_skl))) ),
inference(resolution,[status(thm)],[f625,f121]) ).
fof(f662,plain,
( in(sK13_skl,relation_rng(sK11_skl))
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f125,f102]) ).
fof(f664,definition,
( sQ31_spl
<=> in(sK13_skl,relation_rng(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f665,plain,
( ~ sQ31_spl
| in(sK13_skl,relation_rng(sK11_skl)) ),
inference(component_clause,[status(thm)],[f664]) ).
fof(f667,plain,
( sQ31_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f662,f536,f664]) ).
fof(f670,plain,
! [X0] :
( ~ sQ31_spl
| in(sK13_skl,set_union2(X0,relation_rng(sK11_skl))) ),
inference(resolution,[status(thm)],[f665,f121]) ).
fof(f679,plain,
( sQ25_spl
| ~ sQ28_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f505,f649]) ).
fof(f688,plain,
( sQ25_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f679]) ).
fof(f715,plain,
( ~ sQ31_spl
| in(sK13_skl,relation_field(sK11_skl)) ),
inference(paramodulation,[status(thm)],[f128,f670]) ).
fof(f720,plain,
( ~ sQ31_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f715,f117]) ).
fof(f721,plain,
( ~ sQ31_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f720]) ).
fof(f722,plain,
$false,
inference(sat_refutation,[status(thm)],[f118,f506,f544,f562,f667,f688,f721]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU180+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 05:53:05 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 0.25/0.52 % Refutation found
% 0.25/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.25/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.59 % Elapsed time: 0.128974 seconds
% 0.25/0.59 % CPU time: 0.299063 seconds
% 0.25/0.59 % Total memory used: 50.816 MB
% 0.25/0.59 % Net memory used: 50.488 MB
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