%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP637+1 : TPTP v9.3.1. Released v3.4.0.
% 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 12:34:54 PM UTC 2026
% Result : Theorem 0.12s 0.47s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of formulae : 112 ( 31 unt; 0 def)
% Number of atoms : 448 ( 23 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 544 ( 208 ~; 214 |; 87 &)
% ( 5 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 168 ( 161 !; 7 ?)
% 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_group_6(C,A,B)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ! [D] :
( m1_group_2(D,A)
=> ! [E] :
( m1_group_2(E,A)
=> ! [F] :
( m1_group_2(F,B)
=> ! [G] :
( m1_group_2(G,B)
=> ( ( m1_group_6(D,A,E)
& u1_struct_0(G) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E))
& u1_struct_0(F) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) )
=> m1_group_6(F,B,G) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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_group_6(C,A,B)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ! [D] :
( m1_group_2(D,A)
=> ! [E] :
( m1_group_2(E,A)
=> ! [F] :
( m1_group_2(F,B)
=> ! [G] :
( m1_group_2(G,B)
=> ( ( m1_group_6(D,A,E)
& u1_struct_0(G) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E))
& u1_struct_0(F) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) )
=> m1_group_6(F,B,G) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ( m1_group_2(B,A)
<=> ( u1_group_1(B) = k1_realset1(u1_group_1(A),u1_struct_0(B))
& r1_tarski(u1_struct_0(B),u1_struct_0(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,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/sandbox/benchmark/theBenchmark.p') ).
fof(f43,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/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A,B] :
( ( m1_group_2(B,A)
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [C] :
( m1_group_6(C,A,B)
<=> m1_group_2(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( m1_group_2(C,A)
=> ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
=> m1_group_2(B,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ? [G] :
( ~ m1_group_6(F,B,G)
& m1_group_6(D,A,E)
& u1_struct_0(G) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E))
& u1_struct_0(F) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D))
& m1_group_2(G,B) )
& m1_group_2(F,B) )
& m1_group_2(E,A) )
& m1_group_2(D,A) )
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,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(f58,plain,
( ~ m1_group_6(sK5_skl,sK1_skl,sK6_skl)
& m1_group_6(sK3_skl,sK0_skl,sK4_skl)
& u1_struct_0(sK6_skl) = k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,u1_struct_0(sK4_skl))
& u1_struct_0(sK5_skl) = k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,u1_struct_0(sK3_skl))
& m1_group_2(sK6_skl,sK1_skl)
& m1_group_2(sK5_skl,sK1_skl)
& m1_group_2(sK4_skl,sK0_skl)
& m1_group_2(sK3_skl,sK0_skl)
& m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
& v1_group_6(sK2_skl,sK0_skl,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,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl),skolemize(D,sK3_skl),skolemize(E,sK4_skl),skolemize(F,sK5_skl),skolemize(G,sK6_skl)],[f57]) ).
fof(f59,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
v3_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f61,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f62,plain,
l1_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f63,plain,
~ v3_struct_0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f64,plain,
v3_group_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f65,plain,
v4_group_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f66,plain,
l1_group_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f67,plain,
v1_funct_1(sK2_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f68,plain,
v1_funct_2(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f70,plain,
m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f71,plain,
m1_group_2(sK3_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f72,plain,
m1_group_2(sK4_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f73,plain,
m1_group_2(sK5_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f74,plain,
m1_group_2(sK6_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f75,plain,
u1_struct_0(sK5_skl) = k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,u1_struct_0(sK3_skl)),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f76,plain,
u1_struct_0(sK6_skl) = k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,u1_struct_0(sK4_skl)),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f77,plain,
m1_group_6(sK3_skl,sK0_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f78,plain,
~ m1_group_6(sK5_skl,sK1_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f84,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)],[f5]) ).
fof(f85,plain,
! [C] :
( v1_relat_1(C)
| ! [A,B] : ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f86,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)],[f85]) ).
fof(f97,plain,
! [A] :
( ! [B] :
( ( m1_group_2(B,A)
<=> ( u1_group_1(B) = k1_realset1(u1_group_1(A),u1_struct_0(B))
& r1_tarski(u1_struct_0(B),u1_struct_0(A)) ) )
| ~ l1_group_1(B)
| ~ v3_group_1(B)
| v3_struct_0(B) )
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f98,plain,
! [A] :
( ! [B] :
( ( ( u1_group_1(B) != k1_realset1(u1_group_1(A),u1_struct_0(B))
| ~ r1_tarski(u1_struct_0(B),u1_struct_0(A))
| m1_group_2(B,A) )
& ( ( u1_group_1(B) = k1_realset1(u1_group_1(A),u1_struct_0(B))
& r1_tarski(u1_struct_0(B),u1_struct_0(A)) )
| ~ m1_group_2(B,A) ) )
| ~ l1_group_1(B)
| ~ v3_group_1(B)
| v3_struct_0(B) )
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( r1_tarski(u1_struct_0(X1),u1_struct_0(X0))
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f107,plain,
! [A] :
( ! [B] :
( ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
| ~ m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f108,plain,
! [X0,X1] :
( ~ v3_struct_0(X1)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( v3_group_1(X1)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f110,plain,
! [X0,X1] :
( l1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f113,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)],[f21]) ).
fof(f114,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)],[f113]) ).
fof(f168,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)],[f43]) ).
fof(f169,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)],[f168]) ).
fof(f170,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)],[f169]) ).
fof(f171,plain,
! [A,B] :
( ! [C] :
( m1_group_6(C,A,B)
<=> m1_group_2(C,B) )
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f172,plain,
! [A,B] :
( ! [C] :
( ( ~ m1_group_2(C,B)
| m1_group_6(C,A,B) )
& ( m1_group_2(C,B)
| ~ m1_group_6(C,A,B) ) )
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f171]) ).
fof(f173,plain,
! [A,B] :
( ( ! [C] :
( ~ m1_group_2(C,B)
| m1_group_6(C,A,B) )
& ! [C] :
( m1_group_2(C,B)
| ~ m1_group_6(C,A,B) ) )
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(miniscoping,[status(thm)],[f172]) ).
fof(f174,plain,
! [X0,X1,X2] :
( m1_group_2(X2,X1)
| ~ m1_group_6(X2,X0,X1)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f175,plain,
! [X0,X1,X2] :
( ~ m1_group_2(X2,X1)
| m1_group_6(X2,X0,X1)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f176,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(f177,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)],[f176]) ).
fof(f178,plain,
! [X0,X1,X2] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f177]) ).
fof(f182,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(f183,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)],[f182]) ).
fof(f184,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)],[f183]) ).
fof(f199,plain,
! [A] :
( ! [B] :
( ! [C] :
( m1_group_2(B,C)
| ~ r1_tarski(u1_struct_0(B),u1_struct_0(C))
| ~ m1_group_2(C,A) )
| ~ m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f200,plain,
! [X0,X1,X2] :
( m1_group_2(X1,X2)
| ~ r1_tarski(u1_struct_0(X1),u1_struct_0(X2))
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f210,plain,
! [X0,X1] :
( r1_tarski(u1_struct_0(X1),u1_struct_0(X0))
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f99,f108]) ).
fof(f212,plain,
! [X0,X1] :
( r1_tarski(u1_struct_0(X1),u1_struct_0(X0))
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X1)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f109]) ).
fof(f213,plain,
m1_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)),
inference(resolution,[status(thm)],[f70,f178]) ).
fof(f227,plain,
! [X0] :
( v3_group_1(X0)
| ~ m1_group_2(X0,sK0_skl)
| ~ l1_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f109,f60]) ).
fof(f229,plain,
! [X0] :
( v3_group_1(X0)
| ~ m1_group_2(X0,sK0_skl)
| ~ l1_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f59]) ).
fof(f234,plain,
! [X0] :
( v3_group_1(X0)
| ~ m1_group_2(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f229,f62]) ).
fof(f236,plain,
v3_group_1(sK4_skl),
inference(resolution,[status(thm)],[f234,f72]) ).
fof(f242,plain,
! [X0] :
( l1_group_1(X0)
| ~ m1_group_2(X0,sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f110,f62]) ).
fof(f244,plain,
! [X0] :
( l1_group_1(X0)
| ~ m1_group_2(X0,sK0_skl)
| ~ v3_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f242,f59]) ).
fof(f254,plain,
! [X0] :
( l1_group_1(X0)
| ~ m1_group_2(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f244,f60]) ).
fof(f255,plain,
l1_group_1(sK4_skl),
inference(resolution,[status(thm)],[f254,f72]) ).
fof(f256,plain,
l1_group_1(sK3_skl),
inference(resolution,[status(thm)],[f254,f71]) ).
fof(f299,plain,
( m1_group_2(sK3_skl,sK4_skl)
| ~ m1_group_2(sK4_skl,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)],[f174,f77]) ).
fof(f300,plain,
( m1_group_2(sK3_skl,sK4_skl)
| ~ m1_group_2(sK4_skl,sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f299,f59]) ).
fof(f316,plain,
! [X0,X1,X2] :
( v1_relat_1(X0)
| ~ m2_relset_1(X0,X1,X2) ),
inference(resolution,[status(thm)],[f114,f86]) ).
fof(f354,plain,
( m1_group_2(sK3_skl,sK4_skl)
| ~ m1_group_2(sK4_skl,sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl) ),
inference(resolution,[status(thm)],[f300,f61]) ).
fof(f355,plain,
( m1_group_2(sK3_skl,sK4_skl)
| ~ m1_group_2(sK4_skl,sK0_skl)
| ~ l1_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f354,f60]) ).
fof(f388,plain,
! [X0,X1] :
( ~ m1_group_2(X1,X0)
| m1_group_6(X1,sK1_skl,X0)
| ~ m1_group_2(X0,sK1_skl)
| ~ l1_group_1(sK1_skl)
| ~ v3_group_1(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f175,f65]) ).
fof(f390,plain,
! [X0,X1] :
( ~ m1_group_2(X1,X0)
| m1_group_6(X1,sK1_skl,X0)
| ~ m1_group_2(X0,sK1_skl)
| ~ l1_group_1(sK1_skl)
| ~ v3_group_1(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f388,f63]) ).
fof(f392,plain,
! [X0,X1] :
( m1_group_2(X0,X1)
| ~ r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_group_2(X1,sK1_skl)
| ~ m1_group_2(X0,sK1_skl)
| ~ l1_group_1(sK1_skl)
| ~ v3_group_1(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f200,f65]) ).
fof(f394,plain,
! [X0,X1] :
( m1_group_2(X0,X1)
| ~ r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_group_2(X1,sK1_skl)
| ~ m1_group_2(X0,sK1_skl)
| ~ l1_group_1(sK1_skl)
| ~ v3_group_1(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f392,f63]) ).
fof(f407,plain,
v1_relat_1(sK2_skl),
inference(resolution,[status(thm)],[f316,f70]) ).
fof(f452,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)],[f170,f68]) ).
fof(f455,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)) ),
inference(forward_subsumption_resolution,[status(thm)],[f452,f67]) ).
fof(f456,plain,
( m1_group_2(sK3_skl,sK4_skl)
| ~ l1_group_1(sK0_skl) ),
inference(resolution,[status(thm)],[f355,f72]) ).
fof(f457,plain,
m1_group_2(sK3_skl,sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f456,f62]) ).
fof(f460,plain,
! [X0,X1] :
( ~ m1_group_2(X1,X0)
| m1_group_6(X1,sK1_skl,X0)
| ~ m1_group_2(X0,sK1_skl)
| ~ l1_group_1(sK1_skl) ),
inference(resolution,[status(thm)],[f390,f64]) ).
fof(f461,plain,
! [X0,X1] :
( ~ m1_group_2(X1,X0)
| m1_group_6(X1,sK1_skl,X0)
| ~ m1_group_2(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f66]) ).
fof(f463,plain,
! [X0] :
( ~ m1_group_2(X0,sK6_skl)
| m1_group_6(X0,sK1_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f461,f74]) ).
fof(f579,plain,
! [X0,X1] :
( m1_group_2(X0,X1)
| ~ r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_group_2(X1,sK1_skl)
| ~ m1_group_2(X0,sK1_skl)
| ~ l1_group_1(sK1_skl) ),
inference(resolution,[status(thm)],[f394,f64]) ).
fof(f580,plain,
! [X0,X1] :
( m1_group_2(X0,X1)
| ~ r1_tarski(u1_struct_0(X0),u1_struct_0(X1))
| ~ m1_group_2(X1,sK1_skl)
| ~ m1_group_2(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f579,f66]) ).
fof(f679,plain,
! [X0] :
( m1_group_2(X0,sK6_skl)
| ~ r1_tarski(u1_struct_0(X0),u1_struct_0(sK6_skl))
| ~ m1_group_2(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f580,f74]) ).
fof(f738,plain,
! [X0] : k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,X0) = k9_relat_1(sK2_skl,X0),
inference(resolution,[status(thm)],[f455,f213]) ).
fof(f739,plain,
u1_struct_0(sK6_skl) = k9_relat_1(sK2_skl,u1_struct_0(sK4_skl)),
inference(backward_demodulation,[status(thm)],[f738,f76]) ).
fof(f740,plain,
u1_struct_0(sK5_skl) = k9_relat_1(sK2_skl,u1_struct_0(sK3_skl)),
inference(backward_demodulation,[status(thm)],[f738,f75]) ).
fof(f755,plain,
! [X0] :
( r1_tarski(k9_relat_1(sK2_skl,X0),u1_struct_0(sK6_skl))
| ~ r1_tarski(X0,u1_struct_0(sK4_skl))
| ~ v1_relat_1(sK2_skl) ),
inference(paramodulation,[status(thm)],[f739,f184]) ).
fof(f757,plain,
! [X0] :
( r1_tarski(k9_relat_1(sK2_skl,X0),u1_struct_0(sK6_skl))
| ~ r1_tarski(X0,u1_struct_0(sK4_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f755,f407]) ).
fof(f768,plain,
( r1_tarski(u1_struct_0(sK5_skl),u1_struct_0(sK6_skl))
| ~ r1_tarski(u1_struct_0(sK3_skl),u1_struct_0(sK4_skl)) ),
inference(paramodulation,[status(thm)],[f740,f757]) ).
fof(f798,plain,
( m1_group_2(sK5_skl,sK6_skl)
| ~ m1_group_2(sK5_skl,sK1_skl)
| ~ r1_tarski(u1_struct_0(sK3_skl),u1_struct_0(sK4_skl)) ),
inference(resolution,[status(thm)],[f768,f679]) ).
fof(f800,plain,
( m1_group_2(sK5_skl,sK6_skl)
| ~ r1_tarski(u1_struct_0(sK3_skl),u1_struct_0(sK4_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f798,f73]) ).
fof(f801,plain,
( ~ m1_group_2(sK3_skl,sK4_skl)
| ~ l1_group_1(sK3_skl)
| ~ l1_group_1(sK4_skl)
| ~ v3_group_1(sK4_skl)
| v3_struct_0(sK4_skl)
| m1_group_2(sK5_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f800,f212]) ).
fof(f803,plain,
( ~ m1_group_2(sK3_skl,sK4_skl)
| ~ l1_group_1(sK3_skl)
| ~ l1_group_1(sK4_skl)
| v3_struct_0(sK4_skl)
| m1_group_2(sK5_skl,sK6_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f801,f236]) ).
fof(f874,plain,
( ~ l1_group_1(sK3_skl)
| ~ l1_group_1(sK4_skl)
| v3_struct_0(sK4_skl)
| m1_group_2(sK5_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f803,f457]) ).
fof(f875,plain,
( ~ l1_group_1(sK3_skl)
| v3_struct_0(sK4_skl)
| m1_group_2(sK5_skl,sK6_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f874,f255]) ).
fof(f876,plain,
( v3_struct_0(sK4_skl)
| m1_group_2(sK5_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f875,f256]) ).
fof(f877,plain,
( m1_group_6(sK5_skl,sK1_skl,sK6_skl)
| v3_struct_0(sK4_skl) ),
inference(resolution,[status(thm)],[f876,f463]) ).
fof(f881,plain,
v3_struct_0(sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f877,f78]) ).
fof(f882,plain,
! [X0] :
( ~ m1_group_2(sK4_skl,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f881,f108]) ).
fof(f884,plain,
( ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f882,f72]) ).
fof(f885,plain,
( ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f884,f59]) ).
fof(f905,plain,
~ l1_group_1(sK0_skl),
inference(resolution,[status(thm)],[f885,f60]) ).
fof(f906,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f905,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP637+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:23:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.47 % Refutation found
% 0.12/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.49 % Elapsed time: 0.121422 seconds
% 0.12/0.49 % CPU time: 0.617353 seconds
% 0.12/0.49 % Total memory used: 119.403 MB
% 0.12/0.49 % Net memory used: 118.736 MB
%------------------------------------------------------------------------------