%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU243+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 : n018.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 02:19:52 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 106 ( 13 unt; 14 def)
% Number of atoms : 353 ( 46 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 412 ( 165 ~; 187 |; 34 &)
% ( 20 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 15 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 108 ( 98 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> ! [B] :
~ ( ! [C] :
~ ( disjoint(fiber(A,C),B)
& in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_well_founded_in(A,B)
<=> ! [C] :
~ ( ! [D] :
~ ( disjoint(fiber(A,D),C)
& in(D,C) )
& C != empty_set
& subset(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,conjecture,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f37,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f48,plain,
! [A] :
( ( well_founded_relation(A)
<=> ! [B] :
( ? [C] :
( disjoint(fiber(A,C),B)
& in(C,B) )
| B = empty_set
| ~ subset(B,relation_field(A)) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f49,plain,
! [A] :
( ( ( ? [B] :
( ! [C] :
( ~ disjoint(fiber(A,C),B)
| ~ in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) )
| well_founded_relation(A) )
& ( ! [B] :
( ? [C] :
( disjoint(fiber(A,C),B)
& in(C,B) )
| B = empty_set
| ~ subset(B,relation_field(A)) )
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [A] :
( ( ( ( ! [C] :
( ~ disjoint(fiber(A,C),sK1_skl(A))
| ~ in(C,sK1_skl(A)) )
& sK1_skl(A) != empty_set
& subset(sK1_skl(A),relation_field(A)) )
| well_founded_relation(A) )
& ( ! [B] :
( ( disjoint(fiber(A,sK0_skl(B,A)),B)
& in(sK0_skl(B,A),B) )
| B = empty_set
| ~ subset(B,relation_field(A)) )
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(B,A)),skolemize(B,sK1_skl(A))],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X1)
| X1 = empty_set
| ~ subset(X1,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( disjoint(fiber(X0,sK0_skl(X1,X0)),X1)
| X1 = empty_set
| ~ subset(X1,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
! [X0] :
( subset(sK1_skl(X0),relation_field(X0))
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
! [X0] :
( sK1_skl(X0) != empty_set
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f55,plain,
! [X0,X1] :
( ~ disjoint(fiber(X0,X1),sK1_skl(X0))
| ~ in(X1,sK1_skl(X0))
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f56,plain,
! [A] :
( ! [B] :
( is_well_founded_in(A,B)
<=> ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f57,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ! [D] :
( ~ disjoint(fiber(A,D),C)
| ~ in(D,C) )
& C != empty_set
& subset(C,B) )
| is_well_founded_in(A,B) )
& ( ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ! [D] :
( ~ disjoint(fiber(A,D),C)
| ~ in(D,C) )
& C != empty_set
& subset(C,B) )
| is_well_founded_in(A,B) )
& ! [B] :
( ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
! [A] :
( ( ! [B] :
( ( ! [D] :
( ~ disjoint(fiber(A,D),sK3_skl(B,A))
| ~ in(D,sK3_skl(B,A)) )
& sK3_skl(B,A) != empty_set
& subset(sK3_skl(B,A),B) )
| is_well_founded_in(A,B) )
& ! [B] :
( ! [C] :
( ( disjoint(fiber(A,sK2_skl(C,B,A)),C)
& in(sK2_skl(C,B,A),C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(D,sK2_skl(C,B,A)),skolemize(C,sK3_skl(B,A))],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( in(sK2_skl(X2,X1,X0),X2)
| X2 = empty_set
| ~ subset(X2,X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( disjoint(fiber(X0,sK2_skl(X2,X1,X0)),X2)
| X2 = empty_set
| ~ subset(X2,X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
! [X0,X1] :
( subset(sK3_skl(X1,X0),X1)
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f63,plain,
! [X0,X1] :
( sK3_skl(X1,X0) != empty_set
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ disjoint(fiber(X0,X2),sK3_skl(X1,X0))
| ~ in(X2,sK3_skl(X1,X0))
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f69,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f70,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f71,plain,
! [A] :
( ! [B] : ~ empty(set_union2(A,B))
| empty(A) ),
inference(miniscoping,[status(thm)],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f97,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f112,plain,
? [A] :
( ( well_founded_relation(A)
<~> is_well_founded_in(A,relation_field(A)) )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f113,plain,
? [A] :
( ( ~ is_well_founded_in(A,relation_field(A))
| ~ well_founded_relation(A) )
& ( is_well_founded_in(A,relation_field(A))
| well_founded_relation(A) )
& relation(A) ),
inference(NNF_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
( ( ~ is_well_founded_in(sK10_skl,relation_field(sK10_skl))
| ~ well_founded_relation(sK10_skl) )
& ( is_well_founded_in(sK10_skl,relation_field(sK10_skl))
| well_founded_relation(sK10_skl) )
& relation(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(A,sK10_skl)],[f113]) ).
fof(f115,plain,
relation(sK10_skl),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
( is_well_founded_in(sK10_skl,relation_field(sK10_skl))
| well_founded_relation(sK10_skl) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f117,plain,
( ~ is_well_founded_in(sK10_skl,relation_field(sK10_skl))
| ~ well_founded_relation(sK10_skl) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f120,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f121,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f126,definition,
( sQ0_spl
<=> well_founded_relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( ~ sQ0_spl
| well_founded_relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,definition,
( sQ1_spl
<=> is_well_founded_in(sK10_skl,relation_field(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ1_spl
| is_well_founded_in(sK10_skl,relation_field(sK10_skl)) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f131,plain,
( sQ1_spl
| ~ is_well_founded_in(sK10_skl,relation_field(sK10_skl)) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f116,f126,f129]) ).
fof(f133,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f117,f126,f129]) ).
fof(f140,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(paramodulation,[status(thm)],[f47,f97]) ).
fof(f163,plain,
! [X0,X1] :
( in(sK2_skl(X1,X0,sK10_skl),X1)
| X1 = empty_set
| ~ subset(X1,X0)
| ~ is_well_founded_in(sK10_skl,X0) ),
inference(resolution,[status(thm)],[f60,f115]) ).
fof(f167,plain,
! [X0,X1] :
( disjoint(fiber(sK10_skl,sK2_skl(X1,X0,sK10_skl)),X1)
| X1 = empty_set
| ~ subset(X1,X0)
| ~ is_well_founded_in(sK10_skl,X0) ),
inference(resolution,[status(thm)],[f61,f115]) ).
fof(f168,plain,
! [X0] :
( ~ sQ1_spl
| in(sK2_skl(X0,relation_field(sK10_skl),sK10_skl),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK10_skl)) ),
inference(resolution,[status(thm)],[f163,f130]) ).
fof(f169,plain,
( ~ sQ1_spl
| well_founded_relation(sK10_skl)
| ~ relation(sK10_skl)
| in(sK2_skl(sK1_skl(sK10_skl),relation_field(sK10_skl),sK10_skl),sK1_skl(sK10_skl))
| sK1_skl(sK10_skl) = empty_set ),
inference(resolution,[status(thm)],[f168,f53]) ).
fof(f171,definition,
( sQ2_spl
<=> sK1_skl(sK10_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ2_spl
| sK1_skl(sK10_skl) = empty_set ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
( sQ3_spl
<=> in(sK2_skl(sK1_skl(sK10_skl),relation_field(sK10_skl),sK10_skl),sK1_skl(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f177,definition,
( sQ4_spl
<=> relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( sQ4_spl
| ~ relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,plain,
( ~ sQ1_spl
| sQ0_spl
| ~ sQ4_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f169,f171,f174,f177,f126,f129]) ).
fof(f188,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f115]) ).
fof(f189,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f188]) ).
fof(f190,plain,
! [X0] :
( ~ sQ1_spl
| disjoint(fiber(sK10_skl,sK2_skl(X0,relation_field(sK10_skl),sK10_skl)),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK10_skl)) ),
inference(resolution,[status(thm)],[f167,f130]) ).
fof(f199,plain,
! [X0] :
( ~ sQ0_spl
| disjoint(fiber(sK10_skl,sK0_skl(X0,sK10_skl)),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK10_skl))
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f127,f52]) ).
fof(f200,plain,
! [X0] :
( ~ sQ0_spl
| in(sK0_skl(X0,sK10_skl),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK10_skl))
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f127,f51]) ).
fof(f201,definition,
! [X0] :
( sQ8_spl
<=> ( disjoint(fiber(sK10_skl,sK0_skl(X0,sK10_skl)),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK10_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f202,plain,
! [X0] :
( ~ sQ8_spl
| disjoint(fiber(sK10_skl,sK0_skl(X0,sK10_skl)),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK10_skl)) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,plain,
( ~ sQ0_spl
| sQ8_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f199,f177,f201,f126]) ).
fof(f205,definition,
! [X0] :
( sQ9_spl
<=> ( in(sK0_skl(X0,sK10_skl),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK10_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ9_spl
| in(sK0_skl(X0,sK10_skl),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK10_skl)) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( ~ sQ0_spl
| sQ9_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f200,f177,f205,f126]) ).
fof(f209,plain,
( ~ sQ2_spl
| well_founded_relation(sK10_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f172,f54]) ).
fof(f213,plain,
( ~ sQ2_spl
| sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f209,f177,f126,f171]) ).
fof(f230,plain,
! [X0] : ~ in(X0,empty_set),
inference(resolution,[status(thm)],[f122,f69]) ).
fof(f235,plain,
! [X0] :
( subset(sK3_skl(X0,sK10_skl),X0)
| is_well_founded_in(sK10_skl,X0) ),
inference(resolution,[status(thm)],[f62,f115]) ).
fof(f237,plain,
( sQ1_spl
| subset(sK3_skl(relation_field(sK10_skl),sK10_skl),relation_field(sK10_skl)) ),
inference(resolution,[status(thm)],[f235,f131]) ).
fof(f240,plain,
! [X0] :
( ~ sQ8_spl
| ~ in(sK0_skl(sK3_skl(X0,sK10_skl),sK10_skl),sK3_skl(X0,sK10_skl))
| is_well_founded_in(sK10_skl,X0)
| ~ relation(sK10_skl)
| sK3_skl(X0,sK10_skl) = empty_set
| ~ subset(sK3_skl(X0,sK10_skl),relation_field(sK10_skl)) ),
inference(resolution,[status(thm)],[f202,f64]) ).
fof(f242,definition,
! [X0] :
( sQ13_spl
<=> ( ~ in(sK0_skl(sK3_skl(X0,sK10_skl),sK10_skl),sK3_skl(X0,sK10_skl))
| is_well_founded_in(sK10_skl,X0)
| sK3_skl(X0,sK10_skl) = empty_set
| ~ subset(sK3_skl(X0,sK10_skl),relation_field(sK10_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f243,plain,
! [X0] :
( ~ sQ13_spl
| ~ in(sK0_skl(sK3_skl(X0,sK10_skl),sK10_skl),sK3_skl(X0,sK10_skl))
| is_well_founded_in(sK10_skl,X0)
| sK3_skl(X0,sK10_skl) = empty_set
| ~ subset(sK3_skl(X0,sK10_skl),relation_field(sK10_skl)) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,plain,
( ~ sQ8_spl
| ~ sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f240,f242,f177,f201]) ).
fof(f246,definition,
( sQ14_spl
<=> subset(sK1_skl(sK10_skl),relation_field(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( sQ14_spl
| ~ subset(sK1_skl(sK10_skl),relation_field(sK10_skl)) ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f256,plain,
! [X0] :
( ~ empty(X0)
| empty(empty_set) ),
inference(paramodulation,[status(thm)],[f140,f72]) ).
fof(f261,definition,
( sQ16_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f264,definition,
! [X0] :
( sQ17_spl
<=> ~ empty(X0) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f265,plain,
! [X0] :
( ~ sQ17_spl
| ~ empty(X0) ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f267,plain,
( sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f256,f261,f264]) ).
fof(f268,plain,
( ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f69,f265]) ).
fof(f269,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f292,definition,
( sQ20_spl
<=> sK3_skl(relation_field(sK10_skl),sK10_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( ~ sQ20_spl
| sK3_skl(relation_field(sK10_skl),sK10_skl) = empty_set ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,definition,
( sQ21_spl
<=> in(sK0_skl(sK3_skl(relation_field(sK10_skl),sK10_skl),sK10_skl),sK3_skl(relation_field(sK10_skl),sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( ~ sQ20_spl
| is_well_founded_in(sK10_skl,relation_field(sK10_skl))
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f293,f63]) ).
fof(f313,plain,
( ~ sQ20_spl
| sQ1_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f307,f177,f129,f292]) ).
fof(f323,plain,
( ~ sQ1_spl
| ~ in(sK2_skl(sK1_skl(sK10_skl),relation_field(sK10_skl),sK10_skl),sK1_skl(sK10_skl))
| well_founded_relation(sK10_skl)
| ~ relation(sK10_skl)
| sK1_skl(sK10_skl) = empty_set
| ~ subset(sK1_skl(sK10_skl),relation_field(sK10_skl)) ),
inference(resolution,[status(thm)],[f190,f55]) ).
fof(f328,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| sQ0_spl
| ~ sQ4_spl
| sQ2_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f323,f246,f171,f177,f126,f174,f129]) ).
fof(f334,definition,
( sQ26_spl
<=> in(sK2_skl(empty_set,relation_field(sK10_skl),sK10_skl),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( ~ sQ26_spl
| in(sK2_skl(empty_set,relation_field(sK10_skl),sK10_skl),empty_set) ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f345,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f335,f230]) ).
fof(f346,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f345]) ).
fof(f363,plain,
( sQ14_spl
| well_founded_relation(sK10_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f248,f53]) ).
fof(f364,plain,
( sQ14_spl
| sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f363,f177,f126,f246]) ).
fof(f370,plain,
( ~ sQ13_spl
| sQ1_spl
| ~ in(sK0_skl(sK3_skl(relation_field(sK10_skl),sK10_skl),sK10_skl),sK3_skl(relation_field(sK10_skl),sK10_skl))
| is_well_founded_in(sK10_skl,relation_field(sK10_skl))
| sK3_skl(relation_field(sK10_skl),sK10_skl) = empty_set ),
inference(resolution,[status(thm)],[f237,f243]) ).
fof(f371,plain,
( ~ sQ13_spl
| ~ sQ21_spl
| sQ1_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f370,f292,f129,f295,f242]) ).
fof(f373,plain,
( sQ1_spl
| ~ sQ9_spl
| in(sK0_skl(sK3_skl(relation_field(sK10_skl),sK10_skl),sK10_skl),sK3_skl(relation_field(sK10_skl),sK10_skl))
| sK3_skl(relation_field(sK10_skl),sK10_skl) = empty_set ),
inference(resolution,[status(thm)],[f206,f237]) ).
fof(f378,plain,
( sQ1_spl
| ~ sQ9_spl
| sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f373,f292,f295,f205,f129]) ).
fof(f386,plain,
$false,
inference(sat_refutation,[status(thm)],[f132,f133,f180,f189,f204,f208,f213,f245,f267,f269,f313,f328,f346,f364,f371,f378]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU243+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n018.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 06:04:44 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.049780 seconds
% 0.13/0.40 % CPU time: 0.161703 seconds
% 0.13/0.40 % Total memory used: 97.231 MB
% 0.13/0.40 % Net memory used: 97.159 MB
%------------------------------------------------------------------------------