%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP639+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:34:54 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 92 ( 18 unt; 10 def)
% Number of atoms : 334 ( 14 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 386 ( 144 ~; 143 |; 67 &)
% ( 13 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 11 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 117 ( 112 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(k5_group_4(A,D)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(k5_group_4(A,D)))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f6,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( m1_group_2(C,A)
& v1_group_1(C) )
=> ( C = k5_group_4(A,B)
<=> ( ! [D] :
( ( m1_group_2(D,A)
& v1_group_1(D) )
=> ( r1_tarski(B,u1_struct_0(D))
=> m1_group_2(C,D) ) )
& r1_tarski(B,u1_struct_0(C)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( m1_group_2(k5_group_4(A,B),A)
& v1_group_1(k5_group_4(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A,B,C,D] :
( ( m1_relset_1(C,A,B)
& v1_funct_2(C,A,B)
& v1_funct_1(C) )
=> k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(k5_group_4(A,D))))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
& l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f57,plain,
( ~ r1_tarski(k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,sK3_skl),k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,u1_struct_0(k5_group_4(sK0_skl,sK3_skl))))
& m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
& m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
& v1_funct_2(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
& v1_funct_1(sK2_skl)
& l1_group_1(sK1_skl)
& v4_group_1(sK1_skl)
& v3_group_1(sK1_skl)
& ~ v3_struct_0(sK1_skl)
& l1_group_1(sK0_skl)
& v4_group_1(sK0_skl)
& v3_group_1(sK0_skl)
& ~ v3_struct_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl),skolemize(D,sK3_skl)],[f56]) ).
fof(f58,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
v3_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f60,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f61,plain,
l1_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f66,plain,
v1_funct_1(sK2_skl),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f67,plain,
v1_funct_2(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f68,plain,
m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f69,plain,
m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f70,plain,
~ r1_tarski(k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,sK3_skl),k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,u1_struct_0(k5_group_4(sK0_skl,sK3_skl)))),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f78,plain,
! [A,B,C] :
( v1_relat_1(C)
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f79,plain,
! [C] :
( v1_relat_1(C)
| ! [A,B] : ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(miniscoping,[status(thm)],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( v1_relat_1(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f91,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( C = k5_group_4(A,B)
<=> ( ! [D] :
( m1_group_2(C,D)
| ~ r1_tarski(B,u1_struct_0(D))
| ~ m1_group_2(D,A)
| ~ v1_group_1(D) )
& r1_tarski(B,u1_struct_0(C)) ) )
| ~ m1_group_2(C,A)
| ~ v1_group_1(C) )
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f92,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ m1_group_2(C,D)
& r1_tarski(B,u1_struct_0(D))
& m1_group_2(D,A)
& v1_group_1(D) )
| ~ r1_tarski(B,u1_struct_0(C))
| C = k5_group_4(A,B) )
& ( ( ! [D] :
( m1_group_2(C,D)
| ~ r1_tarski(B,u1_struct_0(D))
| ~ m1_group_2(D,A)
| ~ v1_group_1(D) )
& r1_tarski(B,u1_struct_0(C)) )
| C != k5_group_4(A,B) ) )
| ~ m1_group_2(C,A)
| ~ v1_group_1(C) )
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ~ m1_group_2(C,sK4_skl(C,B,A))
& r1_tarski(B,u1_struct_0(sK4_skl(C,B,A)))
& m1_group_2(sK4_skl(C,B,A),A)
& v1_group_1(sK4_skl(C,B,A)) )
| ~ r1_tarski(B,u1_struct_0(C))
| C = k5_group_4(A,B) )
& ( ( ! [D] :
( m1_group_2(C,D)
| ~ r1_tarski(B,u1_struct_0(D))
| ~ m1_group_2(D,A)
| ~ v1_group_1(D) )
& r1_tarski(B,u1_struct_0(C)) )
| C != k5_group_4(A,B) ) )
| ~ m1_group_2(C,A)
| ~ v1_group_1(C) )
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(D,sK4_skl(C,B,A))],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( r1_tarski(X1,u1_struct_0(X2))
| X2 != k5_group_4(X0,X1)
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f106,plain,
! [A,B] :
( ( m1_group_2(k5_group_4(A,B),A)
& v1_group_1(k5_group_4(A,B)) )
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f107,plain,
! [X0,X1] :
( v1_group_1(k5_group_4(X0,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( m1_group_2(k5_group_4(X0,X1),X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f115,plain,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
| ~ m2_relset_1(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f116,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f170,plain,
! [A,B,C,D] :
( k2_funct_2(A,B,C,D) = k9_relat_1(C,D)
| ~ m1_relset_1(C,A,B)
| ~ v1_funct_2(C,A,B)
| ~ v1_funct_1(C) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f171,plain,
! [A,B,C] :
( ! [D] : k2_funct_2(A,B,C,D) = k9_relat_1(C,D)
| ~ m1_relset_1(C,A,B)
| ~ v1_funct_2(C,A,B)
| ~ v1_funct_1(C) ),
inference(miniscoping,[status(thm)],[f170]) ).
fof(f172,plain,
! [X0,X1,X2,X3] :
( k2_funct_2(X1,X2,X0,X3) = k9_relat_1(X0,X3)
| ~ m1_relset_1(X0,X1,X2)
| ~ v1_funct_2(X0,X1,X2)
| ~ v1_funct_1(X0) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f173,plain,
! [A,B,C] :
( ( ~ m1_relset_1(C,A,B)
| m2_relset_1(C,A,B) )
& ( m1_relset_1(C,A,B)
| ~ m2_relset_1(C,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f174,plain,
( ! [A,B,C] :
( ~ m1_relset_1(C,A,B)
| m2_relset_1(C,A,B) )
& ! [A,B,C] :
( m1_relset_1(C,A,B)
| ~ m2_relset_1(C,A,B) ) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f175,plain,
! [X0,X1,X2] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f179,plain,
! [A,B,C] :
( r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B))
| ~ r1_tarski(A,B)
| ~ v1_relat_1(C) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f180,plain,
! [C] :
( ! [A,B] :
( r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B))
| ~ r1_tarski(A,B) )
| ~ v1_relat_1(C) ),
inference(miniscoping,[status(thm)],[f179]) ).
fof(f181,plain,
! [X0,X1,X2] :
( r1_tarski(k9_relat_1(X0,X1),k9_relat_1(X0,X2))
| ~ r1_tarski(X1,X2)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f204,plain,
! [X0,X1] :
( r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1)))
| ~ m1_group_2(k5_group_4(X0,X1),X0)
| ~ v1_group_1(k5_group_4(X0,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f94]) ).
fof(f234,definition,
( sQ4_spl
<=> m1_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f236,plain,
( sQ4_spl
| ~ m1_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)) ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f238,plain,
( sQ4_spl
| ~ m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)) ),
inference(resolution,[status(thm)],[f236,f175]) ).
fof(f239,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f68]) ).
fof(f240,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f239]) ).
fof(f242,plain,
! [X0,X1] :
( r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1)))
| ~ m1_group_2(k5_group_4(X0,X1),X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f204,f107]) ).
fof(f245,plain,
! [X0,X1] :
( r1_tarski(X1,u1_struct_0(k5_group_4(X0,X1)))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f242,f108]) ).
fof(f273,definition,
( sQ9_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f274,plain,
( ~ sQ9_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,definition,
( sQ10_spl
<=> v3_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( sQ10_spl
| ~ v3_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f279,definition,
( sQ11_spl
<=> l1_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( sQ11_spl
| ~ l1_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f286,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f61]) ).
fof(f287,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f286]) ).
fof(f288,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f59]) ).
fof(f289,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f288]) ).
fof(f290,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f274,f58]) ).
fof(f291,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f290]) ).
fof(f399,definition,
( sQ25_spl
<=> v4_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ25_spl
| ~ v4_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f407,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f401,f60]) ).
fof(f408,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f407]) ).
fof(f655,plain,
! [X0] :
( k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,X0) = k9_relat_1(sK2_skl,X0)
| ~ m1_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
| ~ v1_funct_1(sK2_skl) ),
inference(resolution,[status(thm)],[f172,f67]) ).
fof(f658,definition,
( sQ67_spl
<=> v1_funct_1(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f660,plain,
( sQ67_spl
| ~ v1_funct_1(sK2_skl) ),
inference(component_clause,[status(thm)],[f658]) ).
fof(f661,definition,
! [X0] :
( sQ68_spl
<=> k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,X0) = k9_relat_1(sK2_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f662,plain,
! [X0] :
( ~ sQ68_spl
| k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,X0) = k9_relat_1(sK2_skl,X0) ),
inference(component_clause,[status(thm)],[f661]) ).
fof(f664,plain,
( sQ68_spl
| ~ sQ4_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f655,f658,f234,f661]) ).
fof(f667,plain,
( sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f660,f66]) ).
fof(f668,plain,
sQ67_spl,
inference(contradiction_clause,[status(thm)],[f667]) ).
fof(f692,plain,
( ~ sQ68_spl
| ~ r1_tarski(k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,sK3_skl),k9_relat_1(sK2_skl,u1_struct_0(k5_group_4(sK0_skl,sK3_skl)))) ),
inference(backward_demodulation,[status(thm)],[f662,f70]) ).
fof(f695,plain,
( ~ sQ68_spl
| ~ r1_tarski(k9_relat_1(sK2_skl,sK3_skl),k9_relat_1(sK2_skl,u1_struct_0(k5_group_4(sK0_skl,sK3_skl)))) ),
inference(forward_demodulation,[status(thm)],[f662,f692]) ).
fof(f760,plain,
( ~ sQ68_spl
| ~ r1_tarski(sK3_skl,u1_struct_0(k5_group_4(sK0_skl,sK3_skl)))
| ~ v1_relat_1(sK2_skl) ),
inference(resolution,[status(thm)],[f181,f695]) ).
fof(f761,definition,
( sQ82_spl
<=> v1_relat_1(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f763,plain,
( sQ82_spl
| ~ v1_relat_1(sK2_skl) ),
inference(component_clause,[status(thm)],[f761]) ).
fof(f764,definition,
( sQ83_spl
<=> r1_tarski(sK3_skl,u1_struct_0(k5_group_4(sK0_skl,sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f766,plain,
( sQ83_spl
| ~ r1_tarski(sK3_skl,u1_struct_0(k5_group_4(sK0_skl,sK3_skl))) ),
inference(component_clause,[status(thm)],[f764]) ).
fof(f767,plain,
( ~ sQ68_spl
| ~ sQ83_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f760,f761,f764,f661]) ).
fof(f793,plain,
! [X0,X1] :
( sQ82_spl
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(resolution,[status(thm)],[f763,f80]) ).
fof(f834,definition,
( sQ89_spl
<=> m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f836,plain,
( sQ89_spl
| ~ m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
inference(component_clause,[status(thm)],[f834]) ).
fof(f842,plain,
! [X0,X1] :
( sQ82_spl
| ~ m2_relset_1(sK2_skl,X0,X1) ),
inference(resolution,[status(thm)],[f793,f116]) ).
fof(f844,plain,
( sQ82_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f68,f842]) ).
fof(f846,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f844]) ).
fof(f876,plain,
( sQ89_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f836,f69]) ).
fof(f877,plain,
sQ89_spl,
inference(contradiction_clause,[status(thm)],[f876]) ).
fof(f878,plain,
( sQ83_spl
| ~ m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f766,f245]) ).
fof(f879,plain,
( sQ83_spl
| ~ sQ89_spl
| ~ sQ11_spl
| ~ sQ25_spl
| ~ sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f878,f273,f276,f399,f279,f834,f764]) ).
fof(f880,plain,
$false,
inference(sat_refutation,[status(thm)],[f240,f287,f289,f291,f408,f664,f668,f767,f846,f877,f879]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP639+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:27:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.44 % Refutation found
% 0.11/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.47 % Elapsed time: 0.090109 seconds
% 0.11/0.47 % CPU time: 0.461522 seconds
% 0.11/0.47 % Total memory used: 93.362 MB
% 0.11/0.47 % Net memory used: 92.692 MB
%------------------------------------------------------------------------------