%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU048+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 98 ( 8 unt; 14 def)
% Number of atoms : 404 ( 53 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 524 ( 218 ~; 220 |; 53 &)
% ( 22 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 14 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 125 ( 115 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,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/sandbox/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( one_to_one(B)
=> one_to_one(relation_rng_restriction(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( one_to_one(B)
=> one_to_one(relation_rng_restriction(A,B)) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f47,plain,
! [A] :
( ( one_to_one(A)
<=> ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f48,plain,
! [A] :
( ( ( ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [A] :
( ( ( ( sK0_skl(A) != sK1_skl(A)
& apply(A,sK0_skl(A)) = apply(A,sK1_skl(A))
& in(sK1_skl(A),relation_dom(A))
& in(sK0_skl(A),relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(B,sK0_skl(A)),skolemize(C,sK1_skl(A))],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0] :
( in(sK0_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
! [X0] :
( in(sK1_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0] :
( apply(X0,sK0_skl(X0)) = apply(X0,sK1_skl(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,plain,
! [X0] :
( sK0_skl(X0) != sK1_skl(X0)
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f55,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f56,plain,
! [B] :
( ! [A] : relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f67,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)],[f12]) ).
fof(f68,plain,
! [B] :
( ( ! [A] : function(relation_rng_restriction(A,B))
& ! [A] : relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f70,plain,
! [X0,X1] :
( function(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f128,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)],[f33]) ).
fof(f129,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(f130,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)],[f128,f129]) ).
fof(f131,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)],[f130]) ).
fof(f132,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)],[f131]) ).
fof(f133,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( apply(B,sK14_skl(A,C,B)) != apply(C,sK14_skl(A,C,B))
& in(sK14_skl(A,C,B),relation_dom(B)) )
| ( ( sP0_prd(sK13_skl(A,C,B),C,A)
| in(sK13_skl(A,C,B),relation_dom(B)) )
& ( ~ sP0_prd(sK13_skl(A,C,B),C,A)
| ~ in(sK13_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,[sK13_skl,sK14_skl]),skolemize(D,sK13_skl(A,C,B)),skolemize(D,sK14_skl(A,C,B))],[f132]) ).
fof(f134,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)],[f133]) ).
fof(f136,plain,
! [X0,X1,X2,X3] :
( apply(X0,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X0))
| X0 != relation_rng_restriction(X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f144,plain,
? [A,B] :
( ~ one_to_one(relation_rng_restriction(A,B))
& one_to_one(B)
& function(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f145,plain,
? [B] :
( ? [A] : ~ one_to_one(relation_rng_restriction(A,B))
& one_to_one(B)
& function(B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f146,plain,
( ~ one_to_one(relation_rng_restriction(sK16_skl,sK15_skl))
& one_to_one(sK15_skl)
& function(sK15_skl)
& relation(sK15_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(B,sK15_skl),skolemize(A,sK16_skl)],[f145]) ).
fof(f147,plain,
relation(sK15_skl),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
function(sK15_skl),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f149,plain,
one_to_one(sK15_skl),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f150,plain,
~ one_to_one(relation_rng_restriction(sK16_skl,sK15_skl)),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f151,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)],[f129]) ).
fof(f152,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)],[f151]) ).
fof(f153,plain,
! [X0,X1,X2] :
( in(X0,relation_dom(X1))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f156,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)],[f134]) ).
fof(f158,plain,
! [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X1),X2) = apply(X1,X2)
| ~ 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)],[f136]) ).
fof(f160,plain,
! [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X1),X2) = apply(X1,X2)
| ~ 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)],[f158,f57]) ).
fof(f164,plain,
( in(sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl)),relation_dom(relation_rng_restriction(sK16_skl,sK15_skl)))
| ~ function(relation_rng_restriction(sK16_skl,sK15_skl))
| ~ relation(relation_rng_restriction(sK16_skl,sK15_skl)) ),
inference(resolution,[status(thm)],[f51,f150]) ).
fof(f165,definition,
( sQ0_spl
<=> relation(relation_rng_restriction(sK16_skl,sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( sQ0_spl
| ~ relation(relation_rng_restriction(sK16_skl,sK15_skl)) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,definition,
( sQ1_spl
<=> function(relation_rng_restriction(sK16_skl,sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ1_spl
| ~ function(relation_rng_restriction(sK16_skl,sK15_skl)) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
( sQ2_spl
<=> in(sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl)),relation_dom(relation_rng_restriction(sK16_skl,sK15_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ2_spl
| in(sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl)),relation_dom(relation_rng_restriction(sK16_skl,sK15_skl))) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f164,f165,f168,f171]) ).
fof(f175,plain,
( in(sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl)),relation_dom(relation_rng_restriction(sK16_skl,sK15_skl)))
| ~ function(relation_rng_restriction(sK16_skl,sK15_skl))
| ~ relation(relation_rng_restriction(sK16_skl,sK15_skl)) ),
inference(resolution,[status(thm)],[f52,f150]) ).
fof(f176,definition,
( sQ3_spl
<=> in(sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl)),relation_dom(relation_rng_restriction(sK16_skl,sK15_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( ~ sQ3_spl
| in(sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl)),relation_dom(relation_rng_restriction(sK16_skl,sK15_skl))) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f175,f165,f168,f176]) ).
fof(f180,plain,
( sQ1_spl
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f170,f70]) ).
fof(f181,definition,
( sQ4_spl
<=> relation(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( sQ4_spl
| ~ relation(sK15_skl) ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
( sQ5_spl
<=> function(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( sQ5_spl
| ~ function(sK15_skl) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,plain,
( sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f180,f181,f184,f168]) ).
fof(f188,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f148]) ).
fof(f189,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f188]) ).
fof(f190,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f183,f147]) ).
fof(f191,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f192,plain,
( sQ0_spl
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f167,f57]) ).
fof(f194,plain,
( sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f192,f181,f165]) ).
fof(f195,plain,
( ~ sQ2_spl
| apply(relation_rng_restriction(sK16_skl,sK15_skl),sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl))) = apply(sK15_skl,sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl)))
| ~ function(sK15_skl)
| ~ relation(sK15_skl)
| ~ function(relation_rng_restriction(sK16_skl,sK15_skl)) ),
inference(resolution,[status(thm)],[f172,f160]) ).
fof(f197,definition,
( sQ6_spl
<=> apply(relation_rng_restriction(sK16_skl,sK15_skl),sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl))) = apply(sK15_skl,sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl))) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( ~ sQ6_spl
| apply(relation_rng_restriction(sK16_skl,sK15_skl),sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl))) = apply(sK15_skl,sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl))) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,plain,
( ~ sQ2_spl
| sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f195,f168,f181,f184,f197,f171]) ).
fof(f203,plain,
( ~ sQ3_spl
| apply(relation_rng_restriction(sK16_skl,sK15_skl),sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl))) = apply(sK15_skl,sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl)))
| ~ function(sK15_skl)
| ~ relation(sK15_skl)
| ~ function(relation_rng_restriction(sK16_skl,sK15_skl)) ),
inference(resolution,[status(thm)],[f177,f160]) ).
fof(f205,definition,
( sQ7_spl
<=> apply(relation_rng_restriction(sK16_skl,sK15_skl),sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl))) = apply(sK15_skl,sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl))) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ7_spl
| apply(relation_rng_restriction(sK16_skl,sK15_skl),sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl))) = apply(sK15_skl,sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl))) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( ~ sQ3_spl
| sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f203,f168,f181,f184,f205,f176]) ).
fof(f228,plain,
( apply(relation_rng_restriction(sK16_skl,sK15_skl),sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl))) = apply(relation_rng_restriction(sK16_skl,sK15_skl),sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl)))
| ~ function(relation_rng_restriction(sK16_skl,sK15_skl))
| ~ relation(relation_rng_restriction(sK16_skl,sK15_skl)) ),
inference(resolution,[status(thm)],[f53,f150]) ).
fof(f229,definition,
( sQ11_spl
<=> apply(relation_rng_restriction(sK16_skl,sK15_skl),sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl))) = apply(relation_rng_restriction(sK16_skl,sK15_skl),sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( ~ sQ11_spl
| apply(relation_rng_restriction(sK16_skl,sK15_skl),sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl))) = apply(relation_rng_restriction(sK16_skl,sK15_skl),sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl))) ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f232,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f228,f165,f168,f229]) ).
fof(f233,plain,
( ~ sQ11_spl
| ~ sQ6_spl
| apply(sK15_skl,sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl))) = apply(relation_rng_restriction(sK16_skl,sK15_skl),sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl))) ),
inference(forward_demodulation,[status(thm)],[f198,f230]) ).
fof(f234,plain,
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| apply(sK15_skl,sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl))) = apply(sK15_skl,sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl))) ),
inference(forward_demodulation,[status(thm)],[f206,f233]) ).
fof(f235,plain,
( sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl)) != sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl))
| ~ function(relation_rng_restriction(sK16_skl,sK15_skl))
| ~ relation(relation_rng_restriction(sK16_skl,sK15_skl)) ),
inference(resolution,[status(thm)],[f54,f150]) ).
fof(f236,definition,
( sQ12_spl
<=> sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl)) = sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f235,f165,f168,f236]) ).
fof(f241,plain,
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl)) = sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl))
| ~ in(sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl)),relation_dom(sK15_skl))
| ~ in(sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl)),relation_dom(sK15_skl))
| ~ one_to_one(sK15_skl)
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f234,f50]) ).
fof(f245,definition,
( sQ13_spl
<=> one_to_one(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( sQ13_spl
| ~ one_to_one(sK15_skl) ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,definition,
( sQ14_spl
<=> in(sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl)),relation_dom(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f251,definition,
( sQ15_spl
<=> in(sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl)),relation_dom(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ12_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f241,f181,f184,f245,f248,f251,f236,f205,f197,f229]) ).
fof(f344,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)],[f156,f57]) ).
fof(f349,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)],[f153,f344]) ).
fof(f350,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)],[f349,f70]) ).
fof(f352,plain,
( ~ sQ3_spl
| ~ function(sK15_skl)
| ~ relation(sK15_skl)
| in(sK1_skl(relation_rng_restriction(sK16_skl,sK15_skl)),relation_dom(sK15_skl)) ),
inference(resolution,[status(thm)],[f350,f177]) ).
fof(f353,plain,
( ~ sQ2_spl
| ~ function(sK15_skl)
| ~ relation(sK15_skl)
| in(sK0_skl(relation_rng_restriction(sK16_skl,sK15_skl)),relation_dom(sK15_skl)) ),
inference(resolution,[status(thm)],[f350,f172]) ).
fof(f354,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f352,f251,f181,f184,f176]) ).
fof(f355,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f353,f248,f181,f184,f171]) ).
fof(f356,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f247,f149]) ).
fof(f357,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f358,plain,
$false,
inference(sat_refutation,[status(thm)],[f174,f179,f187,f189,f191,f194,f200,f208,f232,f239,f254,f354,f355,f357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU048+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 05:50:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.063663 seconds
% 0.09/0.44 % CPU time: 0.162507 seconds
% 0.09/0.44 % Total memory used: 82.642 MB
% 0.09/0.44 % Net memory used: 82.566 MB
%------------------------------------------------------------------------------