%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG216+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 : n014.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 11:48:58 AM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 77 ( 24 unt; 0 def)
% Number of atoms : 608 ( 31 equ)
% Maximal formula atoms : 38 ( 7 avg)
% Number of connectives : 932 ( 401 ~; 423 |; 89 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 51 ( 48 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( k1_rlvect_1(A) != k2_group_1(A)
=> ( ~ v1_rmod_5(k8_rlvect_2(B,k1_rlvect_1(B),C),A,B)
& ~ v1_rmod_5(k8_rlvect_2(B,C,k1_rlvect_1(B)),A,B) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( k1_rlvect_1(A) != k2_group_1(A)
=> ( ~ v1_rmod_5(k8_rlvect_2(B,k1_rlvect_1(B),C),A,B)
& ~ v1_rmod_5(k8_rlvect_2(B,C,k1_rlvect_1(B)),A,B) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f31,axiom,
! [A] :
( l1_rlvect_1(A)
=> l2_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A] :
( l2_struct_0(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A] :
( l2_struct_0(A)
=> m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_vectsp_2(B,A)
=> l1_rlvect_1(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [A] :
( l3_vectsp_1(A)
=> ( l2_vectsp_1(A)
& l1_rlvect_1(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( v1_rmod_5(k8_rlvect_2(B,C,D),A,B)
=> ( ( D != k1_rlvect_1(B)
& C != k1_rlvect_1(B) )
| k1_rlvect_1(A) = k2_group_1(A) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( v1_rmod_5(k8_rlvect_2(B,k1_rlvect_1(B),C),A,B)
| v1_rmod_5(k8_rlvect_2(B,C,k1_rlvect_1(B)),A,B) )
& k1_rlvect_1(A) != k2_group_1(A)
& m1_subset_1(C,u1_struct_0(B)) )
& l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
& l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f56,plain,
( ( v1_rmod_5(k8_rlvect_2(sK1_skl,k1_rlvect_1(sK1_skl),sK2_skl),sK0_skl,sK1_skl)
| v1_rmod_5(k8_rlvect_2(sK1_skl,sK2_skl,k1_rlvect_1(sK1_skl)),sK0_skl,sK1_skl) )
& k1_rlvect_1(sK0_skl) != k2_group_1(sK0_skl)
& m1_subset_1(sK2_skl,u1_struct_0(sK1_skl))
& l1_vectsp_2(sK1_skl,sK0_skl)
& v5_vectsp_2(sK1_skl,sK0_skl)
& v6_rlvect_1(sK1_skl)
& v5_rlvect_1(sK1_skl)
& v4_rlvect_1(sK1_skl)
& v3_rlvect_1(sK1_skl)
& ~ v3_struct_0(sK1_skl)
& l3_vectsp_1(sK0_skl)
& v8_vectsp_1(sK0_skl)
& v7_vectsp_1(sK0_skl)
& v6_vectsp_1(sK0_skl)
& v4_group_1(sK0_skl)
& v6_rlvect_1(sK0_skl)
& v5_rlvect_1(sK0_skl)
& v4_rlvect_1(sK0_skl)
& v3_rlvect_1(sK0_skl)
& ~ v3_struct_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl)],[f55]) ).
fof(f57,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
v3_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f59,plain,
v4_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f60,plain,
v5_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f61,plain,
v6_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f62,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f63,plain,
v6_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f64,plain,
v7_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f65,plain,
v8_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f66,plain,
l3_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f67,plain,
~ v3_struct_0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f68,plain,
v3_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f69,plain,
v4_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f70,plain,
v5_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f71,plain,
v6_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f72,plain,
v5_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f73,plain,
l1_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f74,plain,
m1_subset_1(sK2_skl,u1_struct_0(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f75,plain,
k1_rlvect_1(sK0_skl) != k2_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f76,plain,
( v1_rmod_5(k8_rlvect_2(sK1_skl,k1_rlvect_1(sK1_skl),sK2_skl),sK0_skl,sK1_skl)
| v1_rmod_5(k8_rlvect_2(sK1_skl,sK2_skl,k1_rlvect_1(sK1_skl)),sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f137,plain,
! [A] :
( l2_struct_0(A)
| ~ l1_rlvect_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f138,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
! [A] :
( l1_struct_0(A)
| ~ l2_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f140,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f173,plain,
! [A] :
( m1_subset_1(k1_rlvect_1(A),u1_struct_0(A))
| ~ l2_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f174,plain,
! [X0] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f180,plain,
! [A] :
( ! [B] :
( l1_rlvect_1(B)
| ~ l1_vectsp_2(B,A) )
| ~ l1_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f181,plain,
! [X0,X1] :
( l1_rlvect_1(X1)
| ~ l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f182,plain,
! [A] :
( ( l2_vectsp_1(A)
& l1_rlvect_1(A) )
| ~ l3_vectsp_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f183,plain,
! [X0] :
( l1_rlvect_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f185,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ( D != k1_rlvect_1(B)
& C != k1_rlvect_1(B) )
| k1_rlvect_1(A) = k2_group_1(A)
| ~ v1_rmod_5(k8_rlvect_2(B,C,D),A,B)
| ~ m1_subset_1(D,u1_struct_0(B)) )
| ~ m1_subset_1(C,u1_struct_0(B)) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) )
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f186,plain,
! [X0,X1,X2,X3] :
( X2 != k1_rlvect_1(X1)
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [X0,X1,X2,X3] :
( X3 != k1_rlvect_1(X1)
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f188,plain,
! [X0,X1,X2] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f186]) ).
fof(f189,plain,
! [X0,X1,X2] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1)
| ~ m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f187]) ).
fof(f190,plain,
( v1_rmod_5(k8_rlvect_2(sK1_skl,k1_rlvect_1(sK1_skl),sK2_skl),sK0_skl,sK1_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ m1_subset_1(k1_rlvect_1(sK1_skl),u1_struct_0(sK1_skl))
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK1_skl))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f189,f76]) ).
fof(f191,plain,
( v1_rmod_5(k8_rlvect_2(sK1_skl,k1_rlvect_1(sK1_skl),sK2_skl),sK0_skl,sK1_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ m1_subset_1(k1_rlvect_1(sK1_skl),u1_struct_0(sK1_skl))
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK1_skl))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f57]) ).
fof(f192,plain,
( v1_rmod_5(k8_rlvect_2(sK1_skl,k1_rlvect_1(sK1_skl),sK2_skl),sK0_skl,sK1_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ m1_subset_1(k1_rlvect_1(sK1_skl),u1_struct_0(sK1_skl))
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK1_skl))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f58]) ).
fof(f193,plain,
( k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK1_skl))
| ~ m1_subset_1(k1_rlvect_1(sK1_skl),u1_struct_0(sK1_skl))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ m1_subset_1(k1_rlvect_1(sK1_skl),u1_struct_0(sK1_skl))
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK1_skl))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl) ),
inference(resolution,[status(thm)],[f192,f188]) ).
fof(f194,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ m1_subset_1(k1_rlvect_1(sK1_skl),u1_struct_0(sK1_skl))
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK1_skl))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f193]) ).
fof(f195,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ m1_subset_1(k1_rlvect_1(sK1_skl),u1_struct_0(sK1_skl))
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK1_skl))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f59]) ).
fof(f196,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ m1_subset_1(k1_rlvect_1(sK1_skl),u1_struct_0(sK1_skl))
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK1_skl))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f60]) ).
fof(f225,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l3_vectsp_1(X0) ),
inference(resolution,[status(thm)],[f183,f138]) ).
fof(f230,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l3_vectsp_1(X0) ),
inference(resolution,[status(thm)],[f225,f140]) ).
fof(f237,plain,
l1_struct_0(sK0_skl),
inference(resolution,[status(thm)],[f230,f66]) ).
fof(f260,plain,
( l1_rlvect_1(sK1_skl)
| ~ l1_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f181,f73]) ).
fof(f263,plain,
l1_rlvect_1(sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f260,f237]) ).
fof(f264,plain,
l2_struct_0(sK1_skl),
inference(resolution,[status(thm)],[f263,f138]) ).
fof(f270,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK1_skl))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ l2_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f174,f196]) ).
fof(f271,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK1_skl))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f264]) ).
fof(f274,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK1_skl))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f271,f61]) ).
fof(f275,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl) ),
inference(resolution,[status(thm)],[f274,f74]) ).
fof(f276,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f275,f62]) ).
fof(f277,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| k1_rlvect_1(sK0_skl) = k2_group_1(sK0_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f276,f63]) ).
fof(f278,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl) ),
inference(resolution,[status(thm)],[f277,f75]) ).
fof(f279,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f64]) ).
fof(f280,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f279,f65]) ).
fof(f281,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl) ),
inference(resolution,[status(thm)],[f280,f72]) ).
fof(f282,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f66]) ).
fof(f283,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f282,f67]) ).
fof(f284,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl) ),
inference(resolution,[status(thm)],[f283,f73]) ).
fof(f285,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f68]) ).
fof(f286,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f285,f69]) ).
fof(f287,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ v5_rlvect_1(sK1_skl) ),
inference(resolution,[status(thm)],[f286,f71]) ).
fof(f288,plain,
( ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f70]) ).
fof(f290,plain,
~ v3_rlvect_1(sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f288,f57]) ).
fof(f291,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f58,f290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG216+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n014.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 13:02:34 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.056149 seconds
% 0.12/0.42 % CPU time: 0.168842 seconds
% 0.12/0.42 % Total memory used: 105.196 MB
% 0.12/0.42 % Net memory used: 105.094 MB
%------------------------------------------------------------------------------