%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU197+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 : n012.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 02:19:38 PM UTC 2026
% Result : Theorem 0.12s 0.49s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 31
% Syntax : Number of formulae : 141 ( 10 unt; 23 def)
% Number of atoms : 471 ( 21 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 604 ( 274 ~; 246 |; 42 &)
% ( 33 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 24 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 207 ( 184 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,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(f12,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f29,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,plain,
! [A,B] :
( ! [C] :
( ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_rng_restriction(A,B) )
& ( ! [D,E] :
( ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D,E] :
( ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_rng_restriction(A,B) )
& ! [A] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( ( ( in(ordered_pair(sK0_skl(A,C,B),sK1_skl(A,C,B)),B)
& in(sK1_skl(A,C,B),A) )
| in(ordered_pair(sK0_skl(A,C,B),sK1_skl(A,C,B)),C) )
& ( ~ in(ordered_pair(sK0_skl(A,C,B),sK1_skl(A,C,B)),B)
| ~ in(sK1_skl(A,C,B),A)
| ~ in(ordered_pair(sK0_skl(A,C,B),sK1_skl(A,C,B)),C) ) )
| C = relation_rng_restriction(A,B) )
& ! [A] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(D,sK0_skl(A,C,B)),skolemize(E,sK1_skl(A,C,B))],[f40]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4] :
( in(X4,X2)
| ~ in(ordered_pair(X3,X4),X1)
| X1 != relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X1)
| X1 != relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X2)
| in(ordered_pair(X3,X4),X1)
| X1 != relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f48,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)],[f5]) ).
fof(f49,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)],[f48]) ).
fof(f50,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)],[f49]) ).
fof(f51,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK4_skl(B,A),sK3_skl(B,A)),A)
| in(sK3_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK3_skl(B,A)),A)
| ~ in(sK3_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK2_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(D,sK2_skl(C,B,A)),skolemize(C,sK3_skl(B,A)),skolemize(D,sK4_skl(B,A))],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X2,X1,X0),X2),X0)
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,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)],[f51]) ).
fof(f57,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f58,plain,
! [B] :
( ! [A] : relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f68,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f69,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f78,plain,
( relation(sK8_skl)
& ~ empty(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f24]) ).
fof(f79,plain,
~ empty(sK8_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,plain,
relation(sK8_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f81,plain,
~ empty(sK9_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f25]) ).
fof(f82,plain,
~ empty(sK9_skl),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
? [A,B,C] :
( ( in(A,relation_rng(relation_rng_restriction(B,C)))
<~> ( in(A,relation_rng(C))
& in(A,B) ) )
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f84,plain,
? [A,B,C] :
( ( ~ in(A,relation_rng(C))
| ~ in(A,B)
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) )
& ( ( in(A,relation_rng(C))
& in(A,B) )
| in(A,relation_rng(relation_rng_restriction(B,C))) )
& relation(C) ),
inference(NNF_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
? [C] :
( ? [A,B] :
( ( ~ in(A,relation_rng(C))
| ~ in(A,B)
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) )
& ( ( in(A,relation_rng(C))
& in(A,B) )
| in(A,relation_rng(relation_rng_restriction(B,C))) ) )
& relation(C) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f86,plain,
( ( ~ in(sK11_skl,relation_rng(sK10_skl))
| ~ in(sK11_skl,sK12_skl)
| ~ in(sK11_skl,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))) )
& ( ( in(sK11_skl,relation_rng(sK10_skl))
& in(sK11_skl,sK12_skl) )
| in(sK11_skl,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))) )
& relation(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(C,sK10_skl),skolemize(A,sK11_skl),skolemize(B,sK12_skl)],[f85]) ).
fof(f87,plain,
relation(sK10_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
( in(sK11_skl,sK12_skl)
| in(sK11_skl,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f89,plain,
( in(sK11_skl,relation_rng(sK10_skl))
| in(sK11_skl,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f90,plain,
( ~ in(sK11_skl,relation_rng(sK10_skl))
| ~ in(sK11_skl,sK12_skl)
| ~ in(sK11_skl,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f93,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f94,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f103,definition,
( sQ0_spl
<=> in(sK11_skl,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ0_spl
| in(sK11_skl,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f105,plain,
( sQ0_spl
| ~ in(sK11_skl,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,definition,
( sQ1_spl
<=> in(sK11_skl,sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( sQ1_spl
| ~ in(sK11_skl,sK12_skl) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f88,f103,f106]) ).
fof(f110,definition,
( sQ2_spl
<=> in(sK11_skl,relation_rng(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( sQ2_spl
| ~ in(sK11_skl,relation_rng(sK10_skl)) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f89,f103,f110]) ).
fof(f114,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f90,f103,f106,f110]) ).
fof(f115,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(ordered_pair(X2,X3),relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f42]) ).
fof(f116,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f43]) ).
fof(f117,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| in(ordered_pair(X2,X3),relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f44]) ).
fof(f118,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X1,relation_rng(X0),X0),X1),X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( in(X2,X3)
| ~ in(ordered_pair(X1,X2),relation_rng_restriction(X3,X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f59]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X1,X2),relation_rng_restriction(X3,X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f116,f59]) ).
fof(f137,plain,
( ~ empty(relation_rng(sK8_skl))
| ~ relation(sK8_skl) ),
inference(resolution,[status(thm)],[f79,f69]) ).
fof(f138,definition,
( sQ3_spl
<=> relation(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ3_spl
| ~ relation(sK8_skl) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,definition,
( sQ4_spl
<=> empty(relation_rng(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( sQ4_spl
| ~ empty(relation_rng(sK8_skl)) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f137,f138,f141]) ).
fof(f145,plain,
( ~ empty(relation_rng(sK9_skl))
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f82,f69]) ).
fof(f146,definition,
( sQ5_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f149,definition,
( sQ6_spl
<=> empty(relation_rng(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f145,f146,f149]) ).
fof(f157,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X1,X2),X0)
| ~ in(X2,X3)
| in(ordered_pair(X1,X2),relation_rng_restriction(X3,X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f59]) ).
fof(f228,definition,
! [X0,X1] :
( sQ13_spl
<=> ( ~ in(ordered_pair(X1,sK11_skl),X0)
| ~ relation(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f229,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ in(ordered_pair(X1,sK11_skl),X0)
| ~ relation(X0)
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f237,definition,
! [X0,X2] :
( sQ14_spl
<=> ( ~ in(ordered_pair(X2,sK11_skl),relation_rng_restriction(sK12_skl,X0))
| ~ relation(relation_rng_restriction(sK12_skl,X0))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f238,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ in(ordered_pair(X1,sK11_skl),relation_rng_restriction(sK12_skl,X0))
| ~ relation(relation_rng_restriction(sK12_skl,X0))
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f252,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ in(ordered_pair(X1,sK11_skl),relation_rng_restriction(sK12_skl,X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f59]) ).
fof(f261,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ in(ordered_pair(X1,sK11_skl),X0)
| ~ in(sK11_skl,sK12_skl)
| ~ relation(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f252,f157]) ).
fof(f265,plain,
( ~ sQ14_spl
| ~ sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f261,f228,f106,f237]) ).
fof(f271,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ in(ordered_pair(X1,sK11_skl),X0)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f229]) ).
fof(f277,plain,
! [X0,X1] :
( ~ sQ13_spl
| empty(X0)
| ~ element(ordered_pair(X1,sK11_skl),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f271,f94]) ).
fof(f292,definition,
! [X0,X1] :
( sQ17_spl
<=> ( ~ in(ordered_pair(X1,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))),X0)
| ~ relation(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f293,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ in(ordered_pair(X1,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))),X0)
| ~ relation(X0)
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f303,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ in(ordered_pair(X1,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))),X0)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f293]) ).
fof(f307,plain,
! [X0,X1] :
( sQ1_spl
| ~ in(ordered_pair(X1,sK11_skl),relation_rng_restriction(sK12_skl,X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f108,f123]) ).
fof(f317,plain,
! [X0] :
( ~ sQ13_spl
| ~ element(ordered_pair(X0,sK11_skl),sK9_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f277,f82]) ).
fof(f318,plain,
! [X0] :
( ~ sQ13_spl
| ~ element(ordered_pair(X0,sK11_skl),sK8_skl)
| ~ relation(sK8_skl) ),
inference(resolution,[status(thm)],[f277,f79]) ).
fof(f319,definition,
! [X0] :
( sQ19_spl
<=> ~ element(ordered_pair(X0,sK11_skl),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( ~ sQ13_spl
| sQ19_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f317,f146,f319,f228]) ).
fof(f323,definition,
! [X0] :
( sQ20_spl
<=> ~ element(ordered_pair(X0,sK11_skl),sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( ~ sQ13_spl
| sQ20_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f318,f138,f323,f228]) ).
fof(f329,plain,
! [X0,X1] :
( ~ sQ17_spl
| empty(X0)
| ~ element(ordered_pair(X1,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f303,f94]) ).
fof(f351,plain,
! [X0] :
( ~ sQ17_spl
| ~ element(ordered_pair(X0,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))),sK9_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f329,f82]) ).
fof(f352,plain,
! [X0] :
( ~ sQ17_spl
| ~ element(ordered_pair(X0,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))),sK8_skl)
| ~ relation(sK8_skl) ),
inference(resolution,[status(thm)],[f329,f79]) ).
fof(f353,definition,
! [X0] :
( sQ22_spl
<=> ~ element(ordered_pair(X0,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( ~ sQ17_spl
| sQ22_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f351,f146,f353,f292]) ).
fof(f357,definition,
! [X0] :
( sQ23_spl
<=> ~ element(ordered_pair(X0,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))),sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f360,plain,
( ~ sQ17_spl
| sQ23_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f352,f138,f357,f292]) ).
fof(f443,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f80]) ).
fof(f444,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f447,plain,
! [X0] :
( ~ sQ17_spl
| sQ4_spl
| ~ element(ordered_pair(X0,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))),relation_rng(sK8_skl))
| ~ relation(relation_rng(sK8_skl)) ),
inference(resolution,[status(thm)],[f143,f329]) ).
fof(f448,plain,
! [X0] :
( ~ sQ13_spl
| sQ4_spl
| ~ element(ordered_pair(X0,sK11_skl),relation_rng(sK8_skl))
| ~ relation(relation_rng(sK8_skl)) ),
inference(resolution,[status(thm)],[f143,f277]) ).
fof(f449,plain,
( sQ4_spl
| ~ empty(relation_rng(relation_rng(sK8_skl)))
| ~ relation(relation_rng(sK8_skl)) ),
inference(resolution,[status(thm)],[f143,f69]) ).
fof(f450,definition,
( sQ25_spl
<=> relation(relation_rng(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f453,definition,
! [X0] :
( sQ26_spl
<=> ~ element(ordered_pair(X0,relation_rng(relation_rng_restriction(sK12_skl,sK10_skl))),relation_rng(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ17_spl
| sQ4_spl
| sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f447,f450,f453,f141,f292]) ).
fof(f457,definition,
! [X0] :
( sQ27_spl
<=> ~ element(ordered_pair(X0,sK11_skl),relation_rng(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( ~ sQ13_spl
| sQ4_spl
| sQ27_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f448,f450,f457,f141,f228]) ).
fof(f461,definition,
( sQ28_spl
<=> empty(relation_rng(relation_rng(sK8_skl))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ4_spl
| ~ sQ28_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f449,f450,f461,f141]) ).
fof(f582,definition,
( sQ32_spl
<=> relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f584,plain,
( sQ32_spl
| ~ relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f582]) ).
fof(f589,definition,
( sQ34_spl
<=> relation(relation_rng_restriction(sK12_skl,sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f591,plain,
( sQ34_spl
| ~ relation(relation_rng_restriction(sK12_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f589]) ).
fof(f594,plain,
( sQ34_spl
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f591,f59]) ).
fof(f596,plain,
( sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f594,f87]) ).
fof(f597,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f596]) ).
fof(f600,plain,
! [X0] :
( sQ1_spl
| ~ in(sK11_skl,relation_rng(relation_rng_restriction(sK12_skl,X0)))
| ~ relation(relation_rng_restriction(sK12_skl,X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f307,f118]) ).
fof(f605,plain,
! [X0] :
( sQ1_spl
| ~ in(sK11_skl,relation_rng(relation_rng_restriction(sK12_skl,X0)))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f600,f59]) ).
fof(f620,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f87]) ).
fof(f621,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f620]) ).
fof(f622,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f605,f104]) ).
fof(f626,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f622,f582,f106,f103]) ).
fof(f670,plain,
! [X0] :
( sQ0_spl
| ~ in(ordered_pair(X0,sK11_skl),relation_rng_restriction(sK12_skl,sK10_skl))
| ~ relation(relation_rng_restriction(sK12_skl,sK10_skl)) ),
inference(resolution,[status(thm)],[f105,f119]) ).
fof(f673,definition,
! [X0] :
( sQ42_spl
<=> ~ in(ordered_pair(X0,sK11_skl),relation_rng_restriction(sK12_skl,sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f674,plain,
! [X0] :
( ~ sQ42_spl
| ~ in(ordered_pair(X0,sK11_skl),relation_rng_restriction(sK12_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f673]) ).
fof(f676,plain,
( sQ0_spl
| sQ42_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f670,f589,f673,f103]) ).
fof(f679,plain,
! [X0] :
( ~ sQ42_spl
| ~ in(ordered_pair(X0,sK11_skl),sK10_skl)
| ~ in(sK11_skl,sK12_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f674,f157]) ).
fof(f684,definition,
! [X0] :
( sQ43_spl
<=> ~ in(ordered_pair(X0,sK11_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f685,plain,
! [X0] :
( ~ sQ43_spl
| ~ in(ordered_pair(X0,sK11_skl),sK10_skl) ),
inference(component_clause,[status(thm)],[f684]) ).
fof(f687,plain,
( ~ sQ42_spl
| sQ43_spl
| ~ sQ1_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f679,f582,f106,f684,f673]) ).
fof(f696,plain,
( ~ sQ43_spl
| ~ in(sK11_skl,relation_rng(sK10_skl))
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f685,f118]) ).
fof(f697,plain,
! [X0,X1] :
( ~ sQ43_spl
| ~ in(ordered_pair(X0,sK11_skl),relation_rng_restriction(X1,sK10_skl))
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f685,f131]) ).
fof(f700,plain,
( ~ sQ43_spl
| ~ sQ2_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f696,f582,f110,f684]) ).
fof(f701,definition,
! [X0,X1] :
( sQ46_spl
<=> ~ in(ordered_pair(X0,sK11_skl),relation_rng_restriction(X1,sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f702,plain,
! [X0,X1] :
( ~ sQ46_spl
| ~ in(ordered_pair(X0,sK11_skl),relation_rng_restriction(X1,sK10_skl)) ),
inference(component_clause,[status(thm)],[f701]) ).
fof(f704,plain,
( ~ sQ43_spl
| sQ46_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f697,f582,f701,f684]) ).
fof(f719,plain,
! [X0] :
( sQ2_spl
| ~ in(ordered_pair(X0,sK11_skl),sK10_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f112,f119]) ).
fof(f722,plain,
( sQ2_spl
| sQ43_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f719,f582,f684,f110]) ).
fof(f743,plain,
! [X0] :
( ~ sQ46_spl
| ~ in(sK11_skl,relation_rng(relation_rng_restriction(X0,sK10_skl)))
| ~ relation(relation_rng_restriction(X0,sK10_skl)) ),
inference(resolution,[status(thm)],[f702,f118]) ).
fof(f865,plain,
( ~ sQ0_spl
| ~ sQ46_spl
| ~ relation(relation_rng_restriction(sK12_skl,sK10_skl)) ),
inference(resolution,[status(thm)],[f743,f104]) ).
fof(f869,plain,
( ~ sQ0_spl
| ~ sQ46_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f865,f589,f701,f103]) ).
fof(f871,plain,
$false,
inference(sat_refutation,[status(thm)],[f109,f113,f114,f144,f152,f265,f322,f326,f356,f360,f444,f456,f460,f464,f597,f621,f626,f676,f687,f700,f704,f722,f869]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU197+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:56:53 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.49 % Refutation found
% 0.12/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.51 % Elapsed time: 0.148865 seconds
% 0.12/0.51 % CPU time: 0.904818 seconds
% 0.12/0.51 % Total memory used: 125.520 MB
% 0.12/0.51 % Net memory used: 123.075 MB
%------------------------------------------------------------------------------