%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP638+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 : 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 12:34:54 PM UTC 2026
% Result : Theorem 0.26s 0.64s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 35
% Syntax : Number of formulae : 176 ( 33 unt; 25 def)
% Number of atoms : 609 ( 22 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 695 ( 262 ~; 287 |; 86 &)
% ( 30 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 41 ( 39 usr; 26 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 153 ( 146 !; 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,B)
=> ! [E] :
( m1_group_2(E,B)
=> ! [F] :
( m1_group_2(F,A)
=> ! [G] :
( m1_group_2(G,A)
=> ( ( m1_group_6(D,B,E)
& u1_struct_0(G) = k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E))
& u1_struct_0(F) = k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) )
=> m1_group_6(F,A,G) ) ) ) ) ) ) ) ),
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_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,B)
=> ! [E] :
( m1_group_2(E,B)
=> ! [F] :
( m1_group_2(F,A)
=> ! [G] :
( m1_group_2(G,A)
=> ( ( m1_group_6(D,B,E)
& u1_struct_0(G) = k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E))
& u1_struct_0(F) = k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) )
=> m1_group_6(F,A,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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B,C,D] :
( ( m1_relset_1(C,A,B)
& v1_funct_1(C) )
=> k3_funct_2(A,B,C,D) = k10_relat_1(C,D) ),
file('/export/starexec/sandbox2/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/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(k10_relat_1(C,A),k10_relat_1(C,B)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ? [G] :
( ~ m1_group_6(F,A,G)
& m1_group_6(D,B,E)
& u1_struct_0(G) = k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E))
& u1_struct_0(F) = k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D))
& m1_group_2(G,A) )
& m1_group_2(F,A) )
& m1_group_2(E,B) )
& m1_group_2(D,B) )
& 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,sK0_skl,sK6_skl)
& m1_group_6(sK3_skl,sK1_skl,sK4_skl)
& u1_struct_0(sK6_skl) = k3_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,u1_struct_0(sK4_skl))
& u1_struct_0(sK5_skl) = k3_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,u1_struct_0(sK3_skl))
& m1_group_2(sK6_skl,sK0_skl)
& m1_group_2(sK5_skl,sK0_skl)
& m1_group_2(sK4_skl,sK1_skl)
& m1_group_2(sK3_skl,sK1_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(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,sK1_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f72,plain,
m1_group_2(sK4_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f73,plain,
m1_group_2(sK5_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f74,plain,
m1_group_2(sK6_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f75,plain,
u1_struct_0(sK5_skl) = k3_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) = k3_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,sK1_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f78,plain,
~ m1_group_6(sK5_skl,sK0_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] :
( k3_funct_2(A,B,C,D) = k10_relat_1(C,D)
| ~ m1_relset_1(C,A,B)
| ~ v1_funct_1(C) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f169,plain,
! [A,B,C] :
( ! [D] : k3_funct_2(A,B,C,D) = k10_relat_1(C,D)
| ~ m1_relset_1(C,A,B)
| ~ v1_funct_1(C) ),
inference(miniscoping,[status(thm)],[f168]) ).
fof(f170,plain,
! [X0,X1,X2,X3] :
( k3_funct_2(X1,X2,X0,X3) = k10_relat_1(X0,X3)
| ~ m1_relset_1(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(k10_relat_1(C,A),k10_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(k10_relat_1(C,A),k10_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(k10_relat_1(X0,X1),k10_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(f224,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(f225,plain,
( ~ sQ4_spl
| m1_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)) ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f226,plain,
( sQ4_spl
| ~ m1_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)) ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f228,plain,
( sQ4_spl
| ~ m2_relset_1(sK2_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl)) ),
inference(resolution,[status(thm)],[f226,f178]) ).
fof(f229,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f70]) ).
fof(f230,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f267,plain,
( ~ m1_group_2(sK5_skl,sK6_skl)
| ~ m1_group_2(sK6_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)],[f175,f78]) ).
fof(f268,definition,
( sQ7_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( ~ sQ7_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f271,definition,
( sQ8_spl
<=> v3_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( sQ8_spl
| ~ v3_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,definition,
( sQ9_spl
<=> v4_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( sQ9_spl
| ~ v4_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,definition,
( sQ10_spl
<=> l1_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f279,plain,
( sQ10_spl
| ~ l1_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,definition,
( sQ11_spl
<=> m1_group_2(sK6_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( sQ11_spl
| ~ m1_group_2(sK6_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,definition,
( sQ12_spl
<=> m1_group_2(sK5_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f285,plain,
( sQ12_spl
| ~ m1_group_2(sK5_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f267,f268,f271,f274,f277,f280,f283]) ).
fof(f287,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f282,f74]) ).
fof(f288,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f289,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f279,f62]) ).
fof(f290,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f289]) ).
fof(f291,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f276,f61]) ).
fof(f292,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f291]) ).
fof(f293,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f273,f60]) ).
fof(f294,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f293]) ).
fof(f295,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f269,f59]) ).
fof(f296,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f319,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(forward_subsumption_resolution,[status(thm)],[f99,f108]) ).
fof(f337,definition,
( sQ21_spl
<=> v3_group_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( sQ21_spl
| ~ v3_group_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,definition,
( sQ22_spl
<=> l1_group_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( sQ22_spl
| ~ l1_group_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f344,definition,
( sQ23_spl
<=> v3_struct_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f345,plain,
( ~ sQ23_spl
| v3_struct_0(sK1_skl) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f355,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f342,f66]) ).
fof(f356,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f357,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f64]) ).
fof(f358,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f359,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f345,f63]) ).
fof(f360,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f359]) ).
fof(f388,plain,
! [X0] :
( sQ12_spl
| ~ r1_tarski(u1_struct_0(sK5_skl),u1_struct_0(sK6_skl))
| ~ m1_group_2(sK6_skl,X0)
| ~ m1_group_2(sK5_skl,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f200,f285]) ).
fof(f389,definition,
! [X0] :
( sQ27_spl
<=> ( ~ m1_group_2(sK6_skl,X0)
| ~ m1_group_2(sK5_skl,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f390,plain,
! [X0] :
( ~ sQ27_spl
| ~ m1_group_2(sK6_skl,X0)
| ~ m1_group_2(sK5_skl,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f392,definition,
( sQ28_spl
<=> r1_tarski(u1_struct_0(sK5_skl),u1_struct_0(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( sQ12_spl
| ~ sQ28_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f388,f389,f392,f283]) ).
fof(f679,plain,
! [X0,X1,X2] :
( k3_funct_2(X0,X1,sK2_skl,X2) = k10_relat_1(sK2_skl,X2)
| ~ m1_relset_1(sK2_skl,X0,X1) ),
inference(resolution,[status(thm)],[f170,f67]) ).
fof(f689,definition,
( sQ68_spl
<=> m1_group_2(sK5_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f691,plain,
( sQ68_spl
| ~ m1_group_2(sK5_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f689]) ).
fof(f694,plain,
( sQ68_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f691,f73]) ).
fof(f695,plain,
sQ68_spl,
inference(contradiction_clause,[status(thm)],[f694]) ).
fof(f699,plain,
! [X0] :
( ~ sQ4_spl
| k3_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK2_skl,X0) = k10_relat_1(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f679,f225]) ).
fof(f841,plain,
( ~ sQ4_spl
| u1_struct_0(sK5_skl) = k10_relat_1(sK2_skl,u1_struct_0(sK3_skl)) ),
inference(backward_demodulation,[status(thm)],[f699,f75]) ).
fof(f842,plain,
( ~ sQ4_spl
| u1_struct_0(sK6_skl) = k10_relat_1(sK2_skl,u1_struct_0(sK4_skl)) ),
inference(backward_demodulation,[status(thm)],[f699,f76]) ).
fof(f849,plain,
! [X0] :
( ~ sQ4_spl
| r1_tarski(u1_struct_0(sK5_skl),k10_relat_1(sK2_skl,X0))
| ~ r1_tarski(u1_struct_0(sK3_skl),X0)
| ~ v1_relat_1(sK2_skl) ),
inference(paramodulation,[status(thm)],[f841,f184]) ).
fof(f850,definition,
( sQ82_spl
<=> v1_relat_1(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f852,plain,
( sQ82_spl
| ~ v1_relat_1(sK2_skl) ),
inference(component_clause,[status(thm)],[f850]) ).
fof(f857,definition,
! [X0] :
( sQ84_spl
<=> ( r1_tarski(u1_struct_0(sK5_skl),k10_relat_1(sK2_skl,X0))
| ~ r1_tarski(u1_struct_0(sK3_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f858,plain,
! [X0] :
( ~ sQ84_spl
| r1_tarski(u1_struct_0(sK5_skl),k10_relat_1(sK2_skl,X0))
| ~ r1_tarski(u1_struct_0(sK3_skl),X0) ),
inference(component_clause,[status(thm)],[f857]) ).
fof(f860,plain,
( ~ sQ4_spl
| sQ84_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f849,f850,f857,f224]) ).
fof(f871,plain,
! [X0,X1] :
( sQ82_spl
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(resolution,[status(thm)],[f852,f86]) ).
fof(f873,plain,
! [X0,X1] :
( sQ82_spl
| ~ m2_relset_1(sK2_skl,X0,X1) ),
inference(resolution,[status(thm)],[f871,f114]) ).
fof(f876,plain,
( sQ82_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f70,f873]) ).
fof(f878,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f876]) ).
fof(f930,definition,
( sQ95_spl
<=> v3_group_1(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f932,plain,
( sQ95_spl
| ~ v3_group_1(sK3_skl) ),
inference(component_clause,[status(thm)],[f930]) ).
fof(f933,definition,
( sQ96_spl
<=> l1_group_1(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f935,plain,
( sQ96_spl
| ~ l1_group_1(sK3_skl) ),
inference(component_clause,[status(thm)],[f933]) ).
fof(f936,definition,
( sQ97_spl
<=> v3_group_1(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f938,plain,
( sQ97_spl
| ~ v3_group_1(sK4_skl) ),
inference(component_clause,[status(thm)],[f936]) ).
fof(f939,definition,
( sQ98_spl
<=> l1_group_1(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f941,plain,
( sQ98_spl
| ~ l1_group_1(sK4_skl) ),
inference(component_clause,[status(thm)],[f939]) ).
fof(f952,definition,
( sQ100_spl
<=> v3_struct_0(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f953,plain,
( ~ sQ100_spl
| v3_struct_0(sK4_skl) ),
inference(component_clause,[status(thm)],[f952]) ).
fof(f970,plain,
( ~ sQ4_spl
| ~ sQ84_spl
| 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)],[f842,f858]) ).
fof(f972,definition,
( sQ105_spl
<=> r1_tarski(u1_struct_0(sK3_skl),u1_struct_0(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f974,plain,
( sQ105_spl
| ~ r1_tarski(u1_struct_0(sK3_skl),u1_struct_0(sK4_skl)) ),
inference(component_clause,[status(thm)],[f972]) ).
fof(f975,plain,
( ~ sQ4_spl
| ~ sQ84_spl
| sQ28_spl
| ~ sQ105_spl ),
inference(split_clause,[status(thm)],[f970,f972,f392,f857,f224]) ).
fof(f977,plain,
! [X0] :
( sQ96_spl
| ~ m1_group_2(sK3_skl,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f935,f110]) ).
fof(f981,plain,
( sQ105_spl
| ~ m1_group_2(sK3_skl,sK4_skl)
| ~ l1_group_1(sK3_skl)
| ~ v3_group_1(sK3_skl)
| ~ l1_group_1(sK4_skl)
| ~ v3_group_1(sK4_skl)
| v3_struct_0(sK4_skl) ),
inference(resolution,[status(thm)],[f974,f319]) ).
fof(f983,definition,
( sQ106_spl
<=> m1_group_2(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f985,plain,
( sQ106_spl
| ~ m1_group_2(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f983]) ).
fof(f986,plain,
( sQ105_spl
| ~ sQ106_spl
| ~ sQ96_spl
| ~ sQ95_spl
| ~ sQ98_spl
| ~ sQ97_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f981,f952,f936,f939,f930,f933,f983,f972]) ).
fof(f1016,plain,
( sQ96_spl
| ~ m1_group_2(sK3_skl,sK1_skl)
| ~ l1_group_1(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f977,f64]) ).
fof(f1027,definition,
( sQ111_spl
<=> m1_group_2(sK3_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1029,plain,
( sQ111_spl
| ~ m1_group_2(sK3_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f1027]) ).
fof(f1030,plain,
( sQ96_spl
| ~ sQ111_spl
| ~ sQ22_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1016,f344,f340,f1027,f933]) ).
fof(f1036,plain,
( sQ111_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1029,f71]) ).
fof(f1037,plain,
sQ111_spl,
inference(contradiction_clause,[status(thm)],[f1036]) ).
fof(f1038,plain,
! [X0] :
( sQ95_spl
| ~ m1_group_2(sK3_skl,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f932,f109]) ).
fof(f1041,plain,
( sQ95_spl
| ~ m1_group_2(sK3_skl,sK1_skl)
| ~ l1_group_1(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f1038,f64]) ).
fof(f1046,plain,
( sQ95_spl
| ~ sQ111_spl
| ~ sQ22_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1041,f344,f340,f1027,f930]) ).
fof(f1049,plain,
! [X0] :
( sQ98_spl
| ~ m1_group_2(sK4_skl,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f941,f110]) ).
fof(f1050,plain,
! [X0] :
( sQ97_spl
| ~ m1_group_2(sK4_skl,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f938,f109]) ).
fof(f1052,plain,
( sQ98_spl
| ~ l1_group_1(sK1_skl)
| ~ v3_group_1(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f1049,f72]) ).
fof(f1057,plain,
( sQ98_spl
| ~ sQ22_spl
| ~ sQ21_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1052,f344,f337,f340,f939]) ).
fof(f1072,plain,
( sQ97_spl
| ~ l1_group_1(sK1_skl)
| ~ v3_group_1(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f1050,f72]) ).
fof(f1077,plain,
( sQ97_spl
| ~ sQ22_spl
| ~ sQ21_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1072,f344,f337,f340,f936]) ).
fof(f1081,plain,
! [X0] :
( ~ sQ100_spl
| ~ m1_group_2(sK4_skl,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f953,f108]) ).
fof(f1095,plain,
( ~ sQ100_spl
| ~ l1_group_1(sK1_skl)
| ~ v3_group_1(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f1081,f72]) ).
fof(f1101,plain,
( ~ sQ100_spl
| ~ sQ22_spl
| ~ sQ21_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1095,f344,f337,f340,f952]) ).
fof(f1171,plain,
! [X0] :
( sQ106_spl
| ~ m1_group_6(sK3_skl,X0,sK4_skl)
| ~ m1_group_2(sK4_skl,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f985,f174]) ).
fof(f1199,plain,
( ~ sQ27_spl
| ~ m1_group_2(sK6_skl,sK0_skl)
| ~ m1_group_2(sK5_skl,sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f390,f61]) ).
fof(f1201,plain,
( ~ sQ27_spl
| ~ sQ11_spl
| ~ sQ68_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1199,f268,f271,f277,f689,f280,f389]) ).
fof(f1409,definition,
( sQ143_spl
<=> m1_group_2(sK4_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1411,plain,
( sQ143_spl
| ~ m1_group_2(sK4_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f1409]) ).
fof(f1417,plain,
( sQ143_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1411,f72]) ).
fof(f1418,plain,
sQ143_spl,
inference(contradiction_clause,[status(thm)],[f1417]) ).
fof(f1482,plain,
( sQ106_spl
| ~ m1_group_6(sK3_skl,sK1_skl,sK4_skl)
| ~ m1_group_2(sK4_skl,sK1_skl)
| ~ l1_group_1(sK1_skl)
| ~ v3_group_1(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f1171,f65]) ).
fof(f1484,definition,
( sQ149_spl
<=> m1_group_6(sK3_skl,sK1_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1486,plain,
( sQ149_spl
| ~ m1_group_6(sK3_skl,sK1_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f1484]) ).
fof(f1487,plain,
( sQ106_spl
| ~ sQ149_spl
| ~ sQ143_spl
| ~ sQ22_spl
| ~ sQ21_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1482,f344,f337,f340,f1409,f1484,f983]) ).
fof(f1492,plain,
( sQ149_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1486,f77]) ).
fof(f1493,plain,
sQ149_spl,
inference(contradiction_clause,[status(thm)],[f1492]) ).
fof(f1494,plain,
$false,
inference(sat_refutation,[status(thm)],[f230,f286,f288,f290,f292,f294,f296,f356,f358,f360,f395,f695,f860,f878,f975,f986,f1030,f1037,f1046,f1057,f1077,f1101,f1201,f1418,f1487,f1493]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP638+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n007.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Sun Sep 20 20:21:50 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.46 % Drodi V4.1.1
% 0.26/0.64 % Refutation found
% 0.26/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.26/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.68 % Elapsed time: 0.212486 seconds
% 0.26/0.68 % CPU time: 1.354027 seconds
% 0.26/0.68 % Total memory used: 124.217 MB
% 0.26/0.68 % Net memory used: 123.151 MB
%------------------------------------------------------------------------------