%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU044+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 : 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 02:19:08 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 30
% Syntax : Number of formulae : 146 ( 24 unt; 15 def)
% Number of atoms : 486 ( 36 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 580 ( 240 ~; 248 |; 55 &)
% ( 23 <=>; 13 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 15 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 197 ( 182 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
<=> ( in(apply(C,B),A)
& in(B,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
<=> ( in(apply(C,B),A)
& in(B,relation_dom(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& ! [D] :
( in(D,relation_dom(B))
<=> ( in(apply(C,D),A)
& in(D,relation_dom(C)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f44,plain,
! [A] : element(sK0_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f5]) ).
fof(f45,plain,
! [X0] : element(sK0_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f47,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f52,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f55,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f56,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f60,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f61,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f69,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
! [C] :
( ~ empty(C)
| ! [B] :
( ~ element(B,powerset(C))
| ! [A] : ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f73,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f77,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f78,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f80,plain,
! [B] :
( ! [A] : relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [A,B] :
( ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f83,plain,
! [B] :
( ( ! [A] : function(relation_rng_restriction(A,B))
& ! [A] : relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f82]) ).
fof(f85,plain,
! [X0,X1] :
( function(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f113,plain,
empty(sK9_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f29]) ).
fof(f114,plain,
empty(sK9_skl),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f117,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f118,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f122,plain,
? [A,B,C] :
( ( in(B,relation_dom(relation_rng_restriction(A,C)))
<~> ( in(apply(C,B),A)
& in(B,relation_dom(C)) ) )
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f123,plain,
? [A,B,C] :
( ( ~ in(apply(C,B),A)
| ~ in(B,relation_dom(C))
| ~ in(B,relation_dom(relation_rng_restriction(A,C))) )
& ( ( in(apply(C,B),A)
& in(B,relation_dom(C)) )
| in(B,relation_dom(relation_rng_restriction(A,C))) )
& function(C)
& relation(C) ),
inference(NNF_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
? [C] :
( ? [A,B] :
( ( ~ in(apply(C,B),A)
| ~ in(B,relation_dom(C))
| ~ in(B,relation_dom(relation_rng_restriction(A,C))) )
& ( ( in(apply(C,B),A)
& in(B,relation_dom(C)) )
| in(B,relation_dom(relation_rng_restriction(A,C))) ) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f123]) ).
fof(f125,plain,
( ( ~ in(apply(sK11_skl,sK13_skl),sK12_skl)
| ~ in(sK13_skl,relation_dom(sK11_skl))
| ~ in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl))) )
& ( ( in(apply(sK11_skl,sK13_skl),sK12_skl)
& in(sK13_skl,relation_dom(sK11_skl)) )
| in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_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)],[f124]) ).
fof(f126,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
function(sK11_skl),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f128,plain,
( in(sK13_skl,relation_dom(sK11_skl))
| in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl))) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f129,plain,
( in(apply(sK11_skl,sK13_skl),sK12_skl)
| in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl))) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f130,plain,
( ~ in(apply(sK11_skl,sK13_skl),sK12_skl)
| ~ in(sK13_skl,relation_dom(sK11_skl))
| ~ in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl))) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f131,plain,
! [A,B] :
( ! [C] :
( ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( in(D,relation_dom(B))
<=> ( in(apply(C,D),A)
& in(D,relation_dom(C)) ) ) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f132,definition,
! [A,C,D] :
( sP0_prd(D,C,A)
<=> ( in(apply(C,D),A)
& in(D,relation_dom(C)) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f133,plain,
! [A,B] :
( ! [C] :
( ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( in(D,relation_dom(B))
<=> sP0_prd(D,C,A) ) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(formula_renaming,[status(thm)],[f131,f132]) ).
fof(f134,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| ? [D] :
( ( sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ( ~ sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) )
| B = relation_rng_restriction(A,C) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( ( ~ sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ( sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) ) )
| B != relation_rng_restriction(A,C) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| ? [D] :
( ( sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ( ~ sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) )
| B = relation_rng_restriction(A,C) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( ~ sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ! [D] :
( sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) )
| B != relation_rng_restriction(A,C) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( apply(B,sK15_skl(A,C,B)) != apply(C,sK15_skl(A,C,B))
& in(sK15_skl(A,C,B),relation_dom(B)) )
| ( ( sP0_prd(sK14_skl(A,C,B),C,A)
| in(sK14_skl(A,C,B),relation_dom(B)) )
& ( ~ sP0_prd(sK14_skl(A,C,B),C,A)
| ~ in(sK14_skl(A,C,B),relation_dom(B)) ) )
| B = relation_rng_restriction(A,C) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( ~ sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ! [D] :
( sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) )
| B != relation_rng_restriction(A,C) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl]),skolemize(D,sK14_skl(A,C,B)),skolemize(D,sK15_skl(A,C,B))],[f135]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( sP0_prd(X3,X1,X2)
| ~ in(X3,relation_dom(X0))
| X0 != relation_rng_restriction(X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X3,X1,X2)
| in(X3,relation_dom(X0))
| X0 != relation_rng_restriction(X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f140,plain,
! [X0,X1,X2] :
( in(sK15_skl(X2,X1,X0),relation_dom(X0))
| ~ sP0_prd(sK14_skl(X2,X1,X0),X1,X2)
| ~ in(sK14_skl(X2,X1,X0),relation_dom(X0))
| X0 = relation_rng_restriction(X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f141,plain,
! [X0,X1,X2] :
( apply(X0,sK15_skl(X2,X1,X0)) != apply(X1,sK15_skl(X2,X1,X0))
| ~ sP0_prd(sK14_skl(X2,X1,X0),X1,X2)
| ~ in(sK14_skl(X2,X1,X0),relation_dom(X0))
| X0 = relation_rng_restriction(X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f144,plain,
! [A,C,D] :
( ( ~ in(apply(C,D),A)
| ~ in(D,relation_dom(C))
| sP0_prd(D,C,A) )
& ( ( in(apply(C,D),A)
& in(D,relation_dom(C)) )
| ~ sP0_prd(D,C,A) ) ),
inference(NNF_transformation,[status(thm)],[f132]) ).
fof(f145,plain,
( ! [A,C,D] :
( ~ in(apply(C,D),A)
| ~ in(D,relation_dom(C))
| sP0_prd(D,C,A) )
& ! [A,C,D] :
( ( in(apply(C,D),A)
& in(D,relation_dom(C)) )
| ~ sP0_prd(D,C,A) ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f146,plain,
! [X0,X1,X2] :
( in(X0,relation_dom(X1))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [X0,X1,X2] :
( in(apply(X1,X0),X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f148,plain,
! [X0,X1,X2] :
( ~ in(apply(X1,X0),X2)
| ~ in(X0,relation_dom(X1))
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f149,definition,
( sQ0_spl
<=> in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ0_spl
| in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl))) ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,definition,
( sQ1_spl
<=> in(sK13_skl,relation_dom(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ1_spl
| in(sK13_skl,relation_dom(sK11_skl)) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f128,f149,f152]) ).
fof(f156,definition,
( sQ2_spl
<=> in(apply(sK11_skl,sK13_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ2_spl
| in(apply(sK11_skl,sK13_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f129,f149,f156]) ).
fof(f160,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f130,f149,f152,f156]) ).
fof(f161,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f162,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X1,X0)
| in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f138]) ).
fof(f168,plain,
function(empty_set),
inference(resolution,[status(thm)],[f38,f47]) ).
fof(f177,definition,
( sQ3_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( sQ3_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,definition,
( sQ4_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f231,plain,
empty(relation_dom(sK9_skl)),
inference(resolution,[status(thm)],[f114,f56]) ).
fof(f235,plain,
! [X0] :
( in(sK0_skl(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[f61,f45]) ).
fof(f295,plain,
sK9_skl = empty_set,
inference(resolution,[status(thm)],[f73,f114]) ).
fof(f297,plain,
relation_dom(sK9_skl) = empty_set,
inference(resolution,[status(thm)],[f73,f231]) ).
fof(f345,plain,
relation_dom(empty_set) = empty_set,
inference(forward_demodulation,[status(thm)],[f295,f297]) ).
fof(f347,plain,
( relation(empty_set)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f345,f57]) ).
fof(f354,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f347,f177,f180]) ).
fof(f355,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f38]) ).
fof(f356,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f362,plain,
! [X0,X1] :
( ~ element(X1,powerset(empty_set))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f71,f38]) ).
fof(f413,plain,
! [X0] :
( ~ in(X0,sK0_skl(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f235,f78]) ).
fof(f423,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f81]) ).
fof(f424,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X1,X0)
| in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f81]) ).
fof(f425,plain,
! [X0,X1,X2] :
( ~ function(X0)
| ~ relation(X0)
| ~ sP0_prd(X1,X0,X2)
| in(X1,relation_dom(relation_rng_restriction(X2,X0)))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f424,f85]) ).
fof(f426,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X1,X0,X2)
| in(X1,relation_dom(relation_rng_restriction(X2,X0)))
| ~ function(X0)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f425]) ).
fof(f427,plain,
! [X0,X1] :
( in(sK15_skl(X1,X0,empty_set),relation_dom(empty_set))
| ~ sP0_prd(sK14_skl(X1,X0,empty_set),X0,X1)
| ~ in(sK14_skl(X1,X0,empty_set),empty_set)
| empty_set = relation_rng_restriction(X1,X0)
| ~ function(X0)
| ~ relation(X0)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f345,f140]) ).
fof(f428,definition,
( sQ23_spl
<=> function(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( sQ23_spl
| ~ function(empty_set) ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f431,definition,
! [X0,X1] :
( sQ24_spl
<=> ( in(sK15_skl(X1,X0,empty_set),relation_dom(empty_set))
| ~ sP0_prd(sK14_skl(X1,X0,empty_set),X0,X1)
| ~ in(sK14_skl(X1,X0,empty_set),empty_set)
| empty_set = relation_rng_restriction(X1,X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( sQ24_spl
| ~ sQ23_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f427,f180,f428,f431]) ).
fof(f435,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f430,f168]) ).
fof(f436,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f435]) ).
fof(f477,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_dom(relation_rng_restriction(X2,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X2,X1))
| in(X0,relation_dom(X1)) ),
inference(resolution,[status(thm)],[f146,f423]) ).
fof(f478,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_dom(relation_rng_restriction(X2,X1)))
| ~ function(X1)
| ~ relation(X1)
| in(X0,relation_dom(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f477,f85]) ).
fof(f479,plain,
! [X0] :
( empty(X0)
| ~ element(X0,powerset(empty_set)) ),
inference(resolution,[status(thm)],[f362,f235]) ).
fof(f490,plain,
empty(sK0_skl(powerset(empty_set))),
inference(resolution,[status(thm)],[f479,f45]) ).
fof(f492,plain,
! [X0] :
( ~ in(X0,powerset(empty_set))
| empty(X0) ),
inference(resolution,[status(thm)],[f479,f118]) ).
fof(f500,plain,
sK0_skl(powerset(empty_set)) = empty_set,
inference(resolution,[status(thm)],[f490,f73]) ).
fof(f507,plain,
( ~ in(powerset(empty_set),empty_set)
| empty(powerset(empty_set)) ),
inference(paramodulation,[status(thm)],[f500,f413]) ).
fof(f508,plain,
( in(empty_set,powerset(empty_set))
| empty(powerset(empty_set)) ),
inference(paramodulation,[status(thm)],[f500,f235]) ).
fof(f510,definition,
( sQ26_spl
<=> empty(powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( ~ sQ26_spl
| empty(powerset(empty_set)) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,definition,
( sQ27_spl
<=> in(powerset(empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( ~ sQ27_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f507,f510,f513]) ).
fof(f517,definition,
( sQ28_spl
<=> in(empty_set,powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f520,plain,
( sQ28_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f508,f510,f517]) ).
fof(f521,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f52]) ).
fof(f522,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f521]) ).
fof(f525,plain,
( empty(powerset(empty_set))
| empty(sK0_skl(powerset(empty_set))) ),
inference(resolution,[status(thm)],[f492,f235]) ).
fof(f528,definition,
( sQ29_spl
<=> empty(sK0_skl(powerset(empty_set))) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f531,plain,
( sQ26_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f525,f528,f510]) ).
fof(f533,plain,
! [X0,X1] :
( apply(empty_set,sK15_skl(X1,X0,empty_set)) != apply(X0,sK15_skl(X1,X0,empty_set))
| ~ sP0_prd(sK14_skl(X1,X0,empty_set),X0,X1)
| ~ in(sK14_skl(X1,X0,empty_set),empty_set)
| empty_set = relation_rng_restriction(X1,X0)
| ~ function(X0)
| ~ relation(X0)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f345,f141]) ).
fof(f534,definition,
! [X0,X1] :
( sQ30_spl
<=> ( apply(empty_set,sK15_skl(X1,X0,empty_set)) != apply(X0,sK15_skl(X1,X0,empty_set))
| ~ sP0_prd(sK14_skl(X1,X0,empty_set),X0,X1)
| ~ in(sK14_skl(X1,X0,empty_set),empty_set)
| empty_set = relation_rng_restriction(X1,X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( sQ30_spl
| ~ sQ23_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f533,f180,f428,f534]) ).
fof(f564,plain,
( ~ sQ0_spl
| ~ function(sK11_skl)
| ~ relation(sK11_skl)
| in(sK13_skl,relation_dom(sK11_skl)) ),
inference(resolution,[status(thm)],[f478,f150]) ).
fof(f565,definition,
( sQ31_spl
<=> relation(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( sQ31_spl
| ~ relation(sK11_skl) ),
inference(component_clause,[status(thm)],[f565]) ).
fof(f568,definition,
( sQ32_spl
<=> function(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( sQ32_spl
| ~ function(sK11_skl) ),
inference(component_clause,[status(thm)],[f568]) ).
fof(f571,plain,
( ~ sQ0_spl
| ~ sQ32_spl
| ~ sQ31_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f564,f152,f565,f568,f149]) ).
fof(f593,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_dom(relation_rng_restriction(X2,X0)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X2,X0))
| in(apply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f147,f423]) ).
fof(f594,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_dom(relation_rng_restriction(X2,X0)))
| ~ function(X0)
| ~ relation(X0)
| in(apply(X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f593,f85]) ).
fof(f595,plain,
! [X0] :
( ~ sQ1_spl
| ~ in(apply(sK11_skl,sK13_skl),X0)
| sP0_prd(sK13_skl,sK11_skl,X0) ),
inference(resolution,[status(thm)],[f148,f153]) ).
fof(f607,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sP0_prd(sK13_skl,sK11_skl,sK12_skl) ),
inference(resolution,[status(thm)],[f595,f157]) ).
fof(f611,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl)))
| ~ function(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f607,f426]) ).
fof(f612,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl
| ~ sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f611,f565,f568,f149,f152,f156]) ).
fof(f613,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f570,f127]) ).
fof(f614,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f613]) ).
fof(f615,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f567,f126]) ).
fof(f616,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f615]) ).
fof(f630,plain,
( ~ sQ0_spl
| ~ function(sK11_skl)
| ~ relation(sK11_skl)
| in(apply(sK11_skl,sK13_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f594,f150]) ).
fof(f632,plain,
( ~ sQ0_spl
| ~ sQ32_spl
| ~ sQ31_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f630,f156,f565,f568,f149]) ).
fof(f633,plain,
$false,
inference(sat_refutation,[status(thm)],[f155,f159,f160,f354,f356,f434,f436,f516,f520,f522,f531,f537,f571,f612,f614,f616,f632]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU044+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:45:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.056976 seconds
% 0.09/0.43 % CPU time: 0.195876 seconds
% 0.09/0.43 % Total memory used: 60.942 MB
% 0.09/0.43 % Net memory used: 60.791 MB
%------------------------------------------------------------------------------