%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG216+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 : Fri Sep 25 12:53:49 PM UTC 2026
% Result : Theorem 0.29s 1.08s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 112 ( 49 unt; 4 def)
% Number of atoms : 562 ( 40 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 742 ( 312 ~; 299 |; 111 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 25 ( 23 usr; 5 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 96 ( 0 sgn 90 !; 6 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( 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) )
=> ! [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) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k1_rlvect_1(X0) != k2_group_1(X0)
=> ( ~ v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1)
& ~ v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_rmod_5) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( 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) )
=> ! [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) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k1_rlvect_1(X0) != k2_group_1(X0)
=> ( ~ v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1)
& ~ v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f31,axiom,
! [X0] :
( l1_rlvect_1(X0)
=> l2_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).
fof(f33,axiom,
! [X0] :
( l2_struct_0(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
fof(f34,axiom,
! [X0] :
( l2_vectsp_1(X0)
=> ( l2_struct_0(X0)
& l1_vectsp_1(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_vectsp_1) ).
fof(f47,axiom,
! [X0] :
( l2_struct_0(X0)
=> m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_rlvect_1) ).
fof(f50,axiom,
! [X0] :
( l1_struct_0(X0)
=> ! [X1] :
( l1_vectsp_2(X1,X0)
=> l1_rlvect_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_2) ).
fof(f51,axiom,
! [X0] :
( l3_vectsp_1(X0)
=> ( l2_vectsp_1(X0)
& l1_rlvect_1(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).
fof(f54,axiom,
! [X0] :
( ( 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) )
=> ! [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) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
=> ( ( X3 != k1_rlvect_1(X1)
& X2 != k1_rlvect_1(X1) )
| k1_rlvect_1(X0) = k2_group_1(X0) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_rmod_5) ).
fof(f59,plain,
? [X0] :
( 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)
& ? [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)
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
& k1_rlvect_1(X0) != k2_group_1(X0)
& ( v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1)
| v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f60,plain,
? [X0] :
( 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)
& ? [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)
& ? [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
& k1_rlvect_1(X0) != k2_group_1(X0)
& ( v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1)
| v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1) ) ) ) ),
inference(flattening,[],[f59]) ).
fof(f78,plain,
! [X0] :
( ~ l1_rlvect_1(X0)
| l2_struct_0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f79,plain,
! [X0] :
( ~ l2_struct_0(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f80,plain,
! [X0] :
( ~ l2_vectsp_1(X0)
| ( l2_struct_0(X0)
& l1_vectsp_1(X0) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f90,plain,
! [X0] :
( ~ l2_struct_0(X0)
| m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f95,plain,
! [X0] :
( ~ l1_struct_0(X0)
| ! [X1] :
( ~ l1_vectsp_2(X1,X0)
| l1_rlvect_1(X1) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f96,plain,
! [X0] :
( ~ l3_vectsp_1(X0)
| ( l2_vectsp_1(X0)
& l1_rlvect_1(X0) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f97,plain,
! [X0] :
( ~ 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)
| ! [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)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| ( X3 != k1_rlvect_1(X1)
& X2 != k1_rlvect_1(X1) )
| k1_rlvect_1(X0) = k2_group_1(X0) ) ) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f98,plain,
! [X0] :
( ~ 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)
| ! [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)
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| ( X3 != k1_rlvect_1(X1)
& X2 != k1_rlvect_1(X1) )
| k1_rlvect_1(X0) = k2_group_1(X0) ) ) ) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
( l3_vectsp_1(sK0)
& v8_vectsp_1(sK0)
& v7_vectsp_1(sK0)
& v6_vectsp_1(sK0)
& v4_group_1(sK0)
& v6_rlvect_1(sK0)
& v5_rlvect_1(sK0)
& v4_rlvect_1(sK0)
& v3_rlvect_1(sK0)
& ~ v3_struct_0(sK0)
& l1_vectsp_2(sK1,sK0)
& v5_vectsp_2(sK1,sK0)
& v6_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v3_rlvect_1(sK1)
& ~ v3_struct_0(sK1)
& m1_subset_1(sK2,u1_struct_0(sK1))
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& ( v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),sK2),sK0,sK1)
| v1_rmod_5(k8_rlvect_2(sK1,sK2,k1_rlvect_1(sK1)),sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f60]) ).
fof(f118,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f119,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f120,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f121,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f122,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f123,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f124,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f125,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f126,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f127,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f128,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f129,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f130,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f131,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f132,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f133,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f134,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f135,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f99]) ).
fof(f136,plain,
k1_rlvect_1(sK0) != k2_group_1(sK0),
inference(cnf_transformation,[],[f99]) ).
fof(f137,plain,
( v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),sK2),sK0,sK1)
| v1_rmod_5(k8_rlvect_2(sK1,sK2,k1_rlvect_1(sK1)),sK0,sK1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f167,plain,
! [X0] :
( ~ l1_rlvect_1(X0)
| l2_struct_0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f168,plain,
! [X0] :
( ~ l2_struct_0(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f169,plain,
! [X0] :
( ~ l2_vectsp_1(X0)
| l2_struct_0(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f186,plain,
! [X0] :
( ~ l2_struct_0(X0)
| m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f189,plain,
! [X0,X1] :
( ~ l1_struct_0(X0)
| ~ l1_vectsp_2(X1,X0)
| l1_rlvect_1(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f190,plain,
! [X0] :
( ~ l3_vectsp_1(X0)
| l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f192,plain,
! [X2,X3,X0,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)
| ~ 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)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| k1_rlvect_1(X1) != X3
| k1_rlvect_1(X0) = k2_group_1(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f193,plain,
! [X2,X3,X0,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)
| ~ 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)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| k1_rlvect_1(X1) != X2
| k1_rlvect_1(X0) = k2_group_1(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f194,plain,
! [X3,X0,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)
| ~ 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)
| ~ m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X3),X0,X1)
| k1_rlvect_1(X0) = k2_group_1(X0) ),
inference(equality_resolution,[],[f193]) ).
fof(f195,plain,
! [X2,X0,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)
| ~ 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)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1)
| k1_rlvect_1(X0) = k2_group_1(X0) ),
inference(equality_resolution,[],[f192]) ).
tcf(c_49,negated_conjecture,
( v1_rmod_5(k8_rlvect_2(sK1,sK2,k1_rlvect_1(sK1)),sK0,sK1)
| v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),sK2),sK0,sK1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_50,negated_conjecture,
k1_rlvect_1(sK0) != k2_group_1(sK0),
inference(cnf_transformation,[],[f136]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f135]) ).
tcf(c_52,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f134]) ).
tcf(c_53,negated_conjecture,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f133]) ).
tcf(c_54,negated_conjecture,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f132]) ).
tcf(c_55,negated_conjecture,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f131]) ).
tcf(c_56,negated_conjecture,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f130]) ).
tcf(c_57,negated_conjecture,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f129]) ).
tcf(c_58,negated_conjecture,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f128]) ).
tcf(c_59,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f127]) ).
tcf(c_60,negated_conjecture,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f126]) ).
tcf(c_61,negated_conjecture,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f125]) ).
tcf(c_62,negated_conjecture,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f124]) ).
tcf(c_63,negated_conjecture,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f123]) ).
tcf(c_64,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f122]) ).
tcf(c_65,negated_conjecture,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f121]) ).
tcf(c_66,negated_conjecture,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f120]) ).
tcf(c_67,negated_conjecture,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f119]) ).
tcf(c_68,negated_conjecture,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f118]) ).
tcf(c_98,plain,
! [X0: $i] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_99,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_101,plain,
! [X0: $i] :
( l2_struct_0(X0)
| ~ l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_117,plain,
! [X0: $i] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] :
( l1_rlvect_1(X0)
| ~ l1_struct_0(X1)
| ~ l1_vectsp_2(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_122,plain,
! [X0: $i] :
( l2_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X0)
| ( k1_rlvect_1(X2) = k2_group_1(X2) )
| ~ l3_vectsp_1(X2)
| ~ v8_vectsp_1(X2)
| ~ v7_vectsp_1(X2)
| ~ v6_vectsp_1(X2)
| ~ v4_group_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,X2)
| ~ v5_vectsp_2(X0,X2)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X1),X2,X0) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| v3_struct_0(X0)
| ( k1_rlvect_1(X2) = k2_group_1(X2) )
| ~ l3_vectsp_1(X2)
| ~ v8_vectsp_1(X2)
| ~ v7_vectsp_1(X2)
| ~ v6_vectsp_1(X2)
| ~ v4_group_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,X2)
| ~ v5_vectsp_2(X0,X2)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ v1_rmod_5(k8_rlvect_2(X0,X1,k1_rlvect_1(X0)),X2,X0) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_129,plain,
( l2_vectsp_1(sK0)
| ~ l3_vectsp_1(sK0) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_132,plain,
( l2_struct_0(sK0)
| ~ l2_vectsp_1(sK0) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_134,plain,
( l1_struct_0(sK0)
| ~ l2_struct_0(sK0) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_825,plain,
! [X0: $i,X1: $i,X2: $i] :
( l2_struct_0(X1)
| ~ l1_struct_0(X2)
| ~ l1_vectsp_2(X0,X2)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_120,c_98]) ).
tcf(c_826,plain,
! [X0: $i,X1: $i] :
( l2_struct_0(X0)
| ~ l1_struct_0(X1)
| ~ l1_vectsp_2(X0,X1) ),
inference(unflattening,[status(thm)],[c_825]) ).
tcf(c_1033,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| ( k1_rlvect_1(X1) = k2_group_1(X1) )
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,X1)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ v1_rmod_5(k8_rlvect_2(X0,X2,k1_rlvect_1(X0)),X1,X0)
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_124]) ).
tcf(c_1034,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| v3_struct_0(sK1)
| ( k1_rlvect_1(sK0) = k2_group_1(sK0) )
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK0)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK0)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK0)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1) ),
inference(unflattening,[status(thm)],[c_1033]) ).
tcf(c_1036,plain,
! [X0: $i] :
( ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1)
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_1034,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_56,c_55,c_54,c_53,c_59,c_58,c_52,c_50,c_1034]) ).
tcf(c_1037,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1) ),
inference(renaming,[status(thm)],[c_1036]) ).
tcf(c_1048,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| ( k1_rlvect_1(X1) = k2_group_1(X1) )
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(X0)
| ~ l1_vectsp_2(X0,X1)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ v1_rmod_5(k8_rlvect_2(X0,k1_rlvect_1(X0),X2),X1,X0)
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_123]) ).
tcf(c_1049,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| v3_struct_0(sK1)
| ( k1_rlvect_1(sK0) = k2_group_1(sK0) )
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK0)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK0)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK0)
| ~ v3_rlvect_1(sK1)
| ~ l1_vectsp_2(sK1,sK0)
| ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1) ),
inference(unflattening,[status(thm)],[c_1048]) ).
tcf(c_1051,plain,
! [X0: $i] :
( ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1)
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_1049,c_68,c_67,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_56,c_55,c_54,c_53,c_59,c_58,c_52,c_50,c_1049]) ).
tcf(c_1052,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1) ),
inference(renaming,[status(thm)],[c_1051]) ).
tcf(c_1069,plain,
! [X0: $i,X1: $i] :
( l2_struct_0(X0)
| ~ l1_struct_0(X1)
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_826]) ).
tcf(c_1070,plain,
( l2_struct_0(sK1)
| ~ l1_struct_0(sK0) ),
inference(unflattening,[status(thm)],[c_1069]) ).
tcf(c_1071,plain,
l2_struct_0(sK1),
inference(global_subsumption_just,[status(thm)],[c_1070,c_68,c_129,c_132,c_134,c_1070]) ).
tcf(c_1185,plain,
! [X0: $i] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_117,c_1071]) ).
tcf(c_1186,plain,
m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1)),
inference(unflattening,[status(thm)],[c_1185]) ).
tcf(c_1247,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X0),sK0,sK1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1052,c_1186]) ).
tcf(c_1248,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ v1_rmod_5(k8_rlvect_2(sK1,X0,k1_rlvect_1(sK1)),sK0,sK1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1037,c_1186]) ).
tcf(c_5142,definition,
iPr_def_10 = k1_rlvect_1(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_5143,definition,
iPr_def_11 = u1_struct_0(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_5147,definition,
iPr_def_15 = k8_rlvect_2(sK1,iPr_def_10,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_5148,definition,
iPr_def_16 = k8_rlvect_2(sK1,sK2,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_5149,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,iPr_def_11)
| ~ v1_rmod_5(k8_rlvect_2(sK1,X0,iPr_def_10),sK0,sK1) ),
inference(demodulation,[status(thm)],[c_1248,c_5143,c_5142]) ).
tcf(c_5150,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,iPr_def_11)
| ~ v1_rmod_5(k8_rlvect_2(sK1,iPr_def_10,X0),sK0,sK1) ),
inference(demodulation,[status(thm)],[c_1247]) ).
tcf(c_5157,negated_conjecture,
m1_subset_1(sK2,iPr_def_11),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_5159,negated_conjecture,
( v1_rmod_5(iPr_def_16,sK0,sK1)
| v1_rmod_5(iPr_def_15,sK0,sK1) ),
inference(demodulation,[status(thm)],[c_49,c_5148,c_5147]) ).
tcf(c_5884,plain,
( ~ m1_subset_1(sK2,iPr_def_11)
| ~ v1_rmod_5(iPr_def_15,sK0,sK1) ),
inference(superposition,[status(thm)],[c_5147,c_5150]) ).
tcf(c_5885,plain,
~ v1_rmod_5(iPr_def_15,sK0,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_5884,c_5157]) ).
tcf(c_5886,plain,
v1_rmod_5(iPr_def_16,sK0,sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_5159,c_5885]) ).
tcf(c_5887,plain,
( ~ m1_subset_1(sK2,iPr_def_11)
| ~ v1_rmod_5(iPr_def_16,sK0,sK1) ),
inference(superposition,[status(thm)],[c_5148,c_5149]) ).
tcf(c_5888,plain,
~ v1_rmod_5(iPr_def_16,sK0,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_5887,c_5157]) ).
tcf(c_5889,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5888,c_5886]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG216+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.36 % Computer : n005.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Fri Sep 25 05:06:17 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.43 % Proving...
% 0.29/1.08 % SZS status Started for theBenchmark.p
% 0.29/1.08 % SZS status Theorem for theBenchmark.p
% 0.29/1.08
% 0.29/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.29/1.08
% 0.29/1.08 % ------ iProver source info
% 0.29/1.08
% 0.29/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 0.29/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.29/1.08 % git: non_committed_changes: false
% 0.29/1.08
% 0.29/1.08 % ------ Parsing...
% 0.29/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.29/1.08
% 0.29/1.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 0 sf_s rm: 16 0s sf_e pe_s pe_e %
% 0.29/1.08
% 0.29/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.29/1.08
% 0.29/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.29/1.08 % ------ Proving...
% 0.29/1.08 % ------ Problem Properties
% 0.29/1.08
% 0.29/1.08 %
% 0.29/1.08 % clauses 68
% 0.29/1.08 % conjectures 5
% 0.29/1.08 % EPR 32
% 0.29/1.08 % Horn 56
% 0.29/1.08 % unary 38
% 0.29/1.08 % binary 18
% 0.29/1.08 % lits 116
% 0.29/1.08 % lits eq 13
% 0.29/1.08 % fd_pure 0
% 0.29/1.08 % fd_pseudo 0
% 0.29/1.08 % fd_cond 1
% 0.29/1.08 % fd_pseudo_cond 1
% 0.29/1.08 % AC symbols 0
% 0.29/1.08
% 0.29/1.08 % ------ Schedule dynamic 5 is on
% 0.29/1.08
% 0.29/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.29/1.08
% 0.29/1.08
% 0.29/1.08 % ------
% 0.29/1.08 % Current options:
% 0.29/1.08 % ------
% 0.29/1.08
% 0.29/1.08
% 0.29/1.08 %
% 0.29/1.08
% 0.29/1.08 % ------ Proving...
% 0.29/1.08 %
% 0.29/1.08
% 0.29/1.08 % SZS status Theorem for theBenchmark.p
% 0.29/1.08
% 0.29/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.29/1.08
% 0.29/1.08
%------------------------------------------------------------------------------