TSTP Solution File: ALG220+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG220+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 18:03:03 EDT 2022
% Result : Theorem 5.04s 5.23s
% Output : Refutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 43
% Syntax : Number of clauses : 72 ( 31 unt; 28 nHn; 72 RR)
% Number of literals : 641 ( 0 equ; 507 neg)
% Maximal clause size : 42 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 26 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v3_rlvect_1(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(2,axiom,
v4_rlvect_1(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(3,axiom,
v5_rlvect_1(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(4,axiom,
v6_rlvect_1(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(5,axiom,
v4_group_1(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(6,axiom,
v7_group_1(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(7,axiom,
v6_vectsp_1(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(8,axiom,
v7_vectsp_1(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(9,axiom,
v8_vectsp_1(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(10,axiom,
v2_vectsp_2(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(11,axiom,
l3_vectsp_1(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(12,axiom,
v3_rlvect_1(skc16),
file('ALG220+1.p',unknown),
[] ).
cnf(13,axiom,
v4_rlvect_1(skc16),
file('ALG220+1.p',unknown),
[] ).
cnf(14,axiom,
v5_rlvect_1(skc16),
file('ALG220+1.p',unknown),
[] ).
cnf(15,axiom,
v6_rlvect_1(skc16),
file('ALG220+1.p',unknown),
[] ).
cnf(27,axiom,
~ v3_struct_0(skc16),
file('ALG220+1.p',unknown),
[] ).
cnf(28,axiom,
~ v3_struct_0(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(29,axiom,
~ v10_vectsp_1(skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(30,axiom,
v3_vectsp_2(skc16,skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(31,axiom,
v5_vectsp_2(skc16,skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(32,axiom,
l1_vectsp_2(skc16,skc15),
file('ALG220+1.p',unknown),
[] ).
cnf(33,axiom,
r1_tarski(skc17,skc18),
file('ALG220+1.p',unknown),
[] ).
cnf(44,axiom,
m1_subset_1(skc18,k1_zfmisc_1(u1_struct_0(skc16))),
file('ALG220+1.p',unknown),
[] ).
cnf(45,axiom,
m1_subset_1(skc17,k1_zfmisc_1(u1_struct_0(skc16))),
file('ALG220+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ l2_struct_0(u)
| l1_struct_0(u) ),
file('ALG220+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ l2_vectsp_1(u)
| l1_vectsp_1(u) ),
file('ALG220+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ l2_vectsp_1(u)
| l2_struct_0(u) ),
file('ALG220+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ l3_vectsp_1(u)
| l2_vectsp_1(u) ),
file('ALG220+1.p',unknown),
[] ).
cnf(57,axiom,
equal(k1_rmod_5(skc15,skc16,skc17),skc16),
file('ALG220+1.p',unknown),
[] ).
cnf(64,axiom,
~ equal(k1_rmod_5(skc15,skc16,skc18),skc16),
file('ALG220+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ l1_struct_0(u)
| ~ l1_vectsp_2(v,u)
| l1_rlvect_1(v) ),
file('ALG220+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ v6_vectsp_1(u)
| ~ v7_group_1(u)
| ~ l1_vectsp_1(u)
| v3_struct_0(u)
| v2_group_1(u) ),
file('ALG220+1.p',unknown),
[] ).
cnf(122,axiom,
( ~ v3_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v6_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ v5_vectsp_2(u,v)
| ~ l1_vectsp_2(u,v)
| ~ m1_rmod_2(w,v,u)
| v3_struct_0(u)
| v3_struct_0(v)
| v6_rlvect_1(w) ),
file('ALG220+1.p',unknown),
[] ).
cnf(123,axiom,
( ~ v3_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v6_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ v5_vectsp_2(u,v)
| ~ l1_vectsp_2(u,v)
| ~ m1_rmod_2(w,v,u)
| v3_struct_0(u)
| v3_struct_0(v)
| v5_rlvect_1(w) ),
file('ALG220+1.p',unknown),
[] ).
cnf(124,axiom,
( ~ v3_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v6_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ v5_vectsp_2(u,v)
| ~ l1_vectsp_2(u,v)
| ~ m1_rmod_2(w,v,u)
| v3_struct_0(u)
| v3_struct_0(v)
| v4_rlvect_1(w) ),
file('ALG220+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ v3_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v6_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ v5_vectsp_2(u,v)
| ~ l1_vectsp_2(u,v)
| ~ m1_rmod_2(w,v,u)
| v3_struct_0(u)
| v3_struct_0(v)
| v3_rlvect_1(w) ),
file('ALG220+1.p',unknown),
[] ).
cnf(126,axiom,
( ~ v3_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v6_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ v5_vectsp_2(u,v)
| ~ l1_vectsp_2(u,v)
| ~ m1_rmod_2(w,v,u)
| v3_struct_0(u)
| v3_struct_0(v)
| l1_vectsp_2(w,v) ),
file('ALG220+1.p',unknown),
[] ).
cnf(127,axiom,
( ~ v3_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v6_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ v5_vectsp_2(u,v)
| ~ l1_vectsp_2(u,v)
| ~ m1_rmod_2(w,v,u)
| v3_struct_0(u)
| v3_struct_0(v)
| v5_vectsp_2(w,v) ),
file('ALG220+1.p',unknown),
[] ).
cnf(128,axiom,
( ~ v3_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v6_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ v3_struct_0(w)
| ~ v5_vectsp_2(u,v)
| ~ l1_vectsp_2(u,v)
| ~ m1_rmod_2(w,v,u)
| v3_struct_0(u)
| v3_struct_0(v) ),
file('ALG220+1.p',unknown),
[] ).
cnf(134,axiom,
( ~ v6_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v3_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v2_vectsp_2(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v7_group_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ v5_vectsp_2(u,v)
| ~ l1_vectsp_2(u,v)
| ~ m1_subset_1(w,k1_zfmisc_1(u1_struct_0(u)))
| v3_struct_0(u)
| v10_vectsp_1(v)
| v3_struct_0(v)
| v3_vectsp_2(k1_rmod_5(v,u,w),v) ),
file('ALG220+1.p',unknown),
[] ).
cnf(135,axiom,
( ~ v6_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v3_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v2_vectsp_2(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v7_group_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ v5_vectsp_2(u,v)
| ~ l1_vectsp_2(u,v)
| ~ m1_subset_1(w,k1_zfmisc_1(u1_struct_0(u)))
| v3_struct_0(u)
| v10_vectsp_1(v)
| v3_struct_0(v)
| m1_rmod_2(k1_rmod_5(v,u,w),v,u) ),
file('ALG220+1.p',unknown),
[] ).
cnf(136,axiom,
( ~ v6_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v3_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v2_vectsp_2(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v7_group_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ r1_tarski(w,x)
| ~ l1_vectsp_2(u,v)
| ~ v5_vectsp_2(u,v)
| ~ m1_subset_1(x,k1_zfmisc_1(u1_struct_0(u)))
| ~ m1_subset_1(w,k1_zfmisc_1(u1_struct_0(u)))
| v3_struct_0(u)
| v10_vectsp_1(v)
| v3_struct_0(v)
| m1_rmod_2(k1_rmod_5(v,u,w),v,k1_rmod_5(v,u,x)) ),
file('ALG220+1.p',unknown),
[] ).
cnf(137,axiom,
( ~ v3_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v6_rlvect_1(u)
| ~ v4_group_1(u)
| ~ v6_vectsp_1(u)
| ~ v7_vectsp_1(u)
| ~ v8_vectsp_1(u)
| ~ l3_vectsp_1(u)
| ~ v3_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v6_rlvect_1(v)
| ~ v3_rlvect_1(w)
| ~ v4_rlvect_1(w)
| ~ v5_rlvect_1(w)
| ~ v6_rlvect_1(w)
| ~ v5_vectsp_2(v,u)
| ~ l1_vectsp_2(v,u)
| ~ v3_vectsp_2(v,u)
| ~ v3_vectsp_2(w,u)
| ~ v5_vectsp_2(w,u)
| ~ l1_vectsp_2(w,u)
| ~ m1_rmod_2(w,u,v)
| ~ m1_rmod_2(v,u,w)
| v3_struct_0(u)
| v3_struct_0(v)
| v3_struct_0(w)
| equal(w,v) ),
file('ALG220+1.p',unknown),
[] ).
cnf(138,plain,
( ~ v6_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v3_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ l1_vectsp_2(u,v)
| ~ v5_vectsp_2(u,v)
| ~ v3_vectsp_2(u,v)
| ~ v3_vectsp_2(w,v)
| ~ m1_rmod_2(w,v,u)
| ~ m1_rmod_2(u,v,w)
| v3_struct_0(u)
| v3_struct_0(v)
| equal(u,w) ),
inference(mrr,[status(thm)],[137,125,124,123,122,127,126,128]),
[iquote('0:MRR:137.9,137.10,137.11,137.12,137.17,137.18,137.26,125.16,124.16,123.16,122.16,127.16,126.16,128.0')] ).
cnf(273,plain,
( ~ v3_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v6_rlvect_1(u)
| ~ v4_group_1(u)
| ~ v7_group_1(u)
| ~ v6_vectsp_1(u)
| ~ v7_vectsp_1(u)
| ~ v8_vectsp_1(u)
| ~ v2_vectsp_2(u)
| ~ l3_vectsp_1(u)
| ~ v3_rlvect_1(skc16)
| ~ v5_rlvect_1(skc16)
| ~ v6_rlvect_1(skc16)
| ~ v5_vectsp_2(skc16,u)
| ~ l1_vectsp_2(skc16,u)
| ~ m1_subset_1(v,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ m1_subset_1(w,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ r1_tarski(v,w)
| v3_struct_0(u)
| v10_vectsp_1(u)
| v3_struct_0(skc16)
| m1_rmod_2(k1_rmod_5(u,skc16,v),u,k1_rmod_5(u,skc16,w)) ),
inference(res,[status(thm),theory(equality)],[13,136]),
[iquote('0:Res:13.0,136.12')] ).
cnf(274,plain,
( ~ v3_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v6_rlvect_1(u)
| ~ v4_group_1(u)
| ~ v7_group_1(u)
| ~ v6_vectsp_1(u)
| ~ v7_vectsp_1(u)
| ~ v8_vectsp_1(u)
| ~ v2_vectsp_2(u)
| ~ l3_vectsp_1(u)
| ~ v3_rlvect_1(skc16)
| ~ v5_rlvect_1(skc16)
| ~ v6_rlvect_1(skc16)
| ~ l1_vectsp_2(skc16,u)
| ~ m1_subset_1(v,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ v5_vectsp_2(skc16,u)
| m1_rmod_2(k1_rmod_5(u,skc16,v),u,skc16)
| v3_struct_0(u)
| v10_vectsp_1(u)
| v3_struct_0(skc16) ),
inference(res,[status(thm),theory(equality)],[13,135]),
[iquote('0:Res:13.0,135.12')] ).
cnf(291,plain,
( ~ v3_struct_0(u)
| ~ v3_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v6_rlvect_1(v)
| ~ v4_group_1(v)
| ~ v6_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v8_vectsp_1(v)
| ~ l3_vectsp_1(v)
| ~ v6_rlvect_1(skc16)
| ~ v5_rlvect_1(skc16)
| ~ v3_rlvect_1(skc16)
| ~ l1_vectsp_2(skc16,v)
| ~ m1_rmod_2(u,v,skc16)
| ~ v5_vectsp_2(skc16,v)
| v3_struct_0(v)
| v3_struct_0(skc16) ),
inference(res,[status(thm),theory(equality)],[13,128]),
[iquote('0:Res:13.0,128.12')] ).
cnf(329,plain,
( ~ l3_vectsp_1(u)
| ~ v8_vectsp_1(u)
| ~ v7_vectsp_1(u)
| ~ v6_vectsp_1(u)
| ~ v4_group_1(u)
| ~ v6_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v3_rlvect_1(u)
| ~ v3_struct_0(v)
| ~ v5_vectsp_2(skc16,u)
| ~ l1_vectsp_2(skc16,u)
| ~ m1_rmod_2(v,u,skc16)
| v3_struct_0(u) ),
inference(mrr,[status(thm)],[291,15,14,12,27]),
[iquote('0:MRR:291.10,291.11,291.12,291.17,15.0,14.0,12.0,27.0')] ).
cnf(337,plain,
( ~ l3_vectsp_1(u)
| ~ v2_vectsp_2(u)
| ~ v8_vectsp_1(u)
| ~ v7_vectsp_1(u)
| ~ v6_vectsp_1(u)
| ~ v7_group_1(u)
| ~ v4_group_1(u)
| ~ v6_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v3_rlvect_1(u)
| ~ m1_subset_1(v,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ v5_vectsp_2(skc16,u)
| ~ l1_vectsp_2(skc16,u)
| v10_vectsp_1(u)
| v3_struct_0(u)
| m1_rmod_2(k1_rmod_5(u,skc16,v),u,skc16) ),
inference(mrr,[status(thm)],[274,12,14,15,27]),
[iquote('0:MRR:274.11,274.12,274.13,274.20,12.0,14.0,15.0,27.0')] ).
cnf(341,plain,
( ~ l3_vectsp_1(u)
| ~ v2_vectsp_2(u)
| ~ v8_vectsp_1(u)
| ~ v7_vectsp_1(u)
| ~ v6_vectsp_1(u)
| ~ v7_group_1(u)
| ~ v4_group_1(u)
| ~ v6_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v3_rlvect_1(u)
| ~ r1_tarski(v,w)
| ~ m1_subset_1(w,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ m1_subset_1(v,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ l1_vectsp_2(skc16,u)
| ~ v5_vectsp_2(skc16,u)
| v10_vectsp_1(u)
| v3_struct_0(u)
| m1_rmod_2(k1_rmod_5(u,skc16,v),u,k1_rmod_5(u,skc16,w)) ),
inference(mrr,[status(thm)],[273,12,14,15,27]),
[iquote('0:MRR:273.11,273.12,273.13,273.21,12.0,14.0,15.0,27.0')] ).
cnf(360,plain,
( ~ l1_struct_0(skc15)
| l1_rlvect_1(skc16) ),
inference(res,[status(thm),theory(equality)],[32,76]),
[iquote('0:Res:32.0,76.1')] ).
cnf(364,plain,
l1_rlvect_1(skc16),
inference(ssi,[status(thm)],[360,53,51,49,10,6,8,5,11,9,7,4,3,2,1]),
[iquote('0:SSi:360.0,53.0,51.0,49.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.1,2.1,1.1')] ).
cnf(427,plain,
( ~ v6_vectsp_1(skc15)
| ~ v7_group_1(skc15)
| ~ l1_vectsp_1(skc15)
| v2_group_1(skc15) ),
inference(res,[status(thm),theory(equality)],[90,28]),
[iquote('0:Res:90.3,28.0')] ).
cnf(433,plain,
v2_group_1(skc15),
inference(ssi,[status(thm)],[427,53,50,10,6,8,5,11,9,7,4,3,2,1]),
[iquote('0:SSi:427.2,427.1,427.0,53.0,50.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.1,1.1')] ).
cnf(1531,plain,
( ~ v6_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v3_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v2_vectsp_2(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v7_group_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ v6_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v3_rlvect_1(u)
| ~ l3_vectsp_1(v)
| ~ v8_vectsp_1(v)
| ~ v7_vectsp_1(v)
| ~ v6_vectsp_1(v)
| ~ v4_group_1(v)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ v5_vectsp_2(u,v)
| ~ l1_vectsp_2(u,v)
| ~ m1_subset_1(w,k1_zfmisc_1(u1_struct_0(u)))
| ~ l1_vectsp_2(u,v)
| ~ v5_vectsp_2(u,v)
| ~ v3_vectsp_2(u,v)
| ~ v3_vectsp_2(k1_rmod_5(v,u,w),v)
| ~ m1_rmod_2(u,v,k1_rmod_5(v,u,w))
| v3_struct_0(u)
| v10_vectsp_1(v)
| v3_struct_0(v)
| v3_struct_0(u)
| v3_struct_0(v)
| equal(k1_rmod_5(v,u,w),u) ),
inference(res,[status(thm),theory(equality)],[135,138]),
[iquote('0:Res:135.21,138.17')] ).
cnf(1536,plain,
( ~ v2_vectsp_2(u)
| ~ v7_group_1(u)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ l3_vectsp_1(u)
| ~ v8_vectsp_1(u)
| ~ v7_vectsp_1(u)
| ~ v6_vectsp_1(u)
| ~ v4_group_1(u)
| ~ v6_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v3_rlvect_1(u)
| ~ m1_subset_1(w,k1_zfmisc_1(u1_struct_0(v)))
| ~ l1_vectsp_2(v,u)
| ~ v5_vectsp_2(v,u)
| ~ v3_vectsp_2(v,u)
| ~ v3_vectsp_2(k1_rmod_5(u,v,w),u)
| ~ m1_rmod_2(v,u,k1_rmod_5(u,v,w))
| v10_vectsp_1(u)
| v3_struct_0(v)
| v3_struct_0(u)
| equal(k1_rmod_5(u,v,w),v) ),
inference(obv,[status(thm),theory(equality)],[1531]),
[iquote('0:Obv:1531.38')] ).
cnf(1537,plain,
( ~ v2_vectsp_2(u)
| ~ v7_group_1(u)
| ~ v6_rlvect_1(v)
| ~ v5_rlvect_1(v)
| ~ v4_rlvect_1(v)
| ~ v3_rlvect_1(v)
| ~ l3_vectsp_1(u)
| ~ v8_vectsp_1(u)
| ~ v7_vectsp_1(u)
| ~ v6_vectsp_1(u)
| ~ v4_group_1(u)
| ~ v6_rlvect_1(u)
| ~ v5_rlvect_1(u)
| ~ v4_rlvect_1(u)
| ~ v3_rlvect_1(u)
| ~ m1_subset_1(w,k1_zfmisc_1(u1_struct_0(v)))
| ~ l1_vectsp_2(v,u)
| ~ v5_vectsp_2(v,u)
| ~ v3_vectsp_2(v,u)
| ~ m1_rmod_2(v,u,k1_rmod_5(u,v,w))
| v10_vectsp_1(u)
| v3_struct_0(v)
| v3_struct_0(u)
| equal(k1_rmod_5(u,v,w),v) ),
inference(mrr,[status(thm)],[1536,134]),
[iquote('0:MRR:1536.19,134.21')] ).
cnf(7347,plain,
( ~ l3_vectsp_1(skc15)
| ~ v2_vectsp_2(skc15)
| ~ v8_vectsp_1(skc15)
| ~ v7_vectsp_1(skc15)
| ~ v6_vectsp_1(skc15)
| ~ v7_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v6_rlvect_1(skc15)
| ~ v5_rlvect_1(skc15)
| ~ v4_rlvect_1(skc15)
| ~ v3_rlvect_1(skc15)
| ~ m1_subset_1(skc17,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ v5_vectsp_2(skc16,skc15)
| ~ l1_vectsp_2(skc16,skc15)
| v10_vectsp_1(skc15)
| v3_struct_0(skc15)
| m1_rmod_2(skc16,skc15,skc16) ),
inference(spr,[status(thm),theory(equality)],[57,337]),
[iquote('0:SpR:57.0,337.16')] ).
cnf(7348,plain,
( ~ l3_vectsp_1(skc15)
| ~ v2_vectsp_2(skc15)
| ~ v8_vectsp_1(skc15)
| ~ v7_vectsp_1(skc15)
| ~ v6_vectsp_1(skc15)
| ~ v7_group_1(skc15)
| ~ v4_group_1(skc15)
| ~ v6_rlvect_1(skc15)
| ~ v5_rlvect_1(skc15)
| ~ v4_rlvect_1(skc15)
| ~ v3_rlvect_1(skc15)
| ~ r1_tarski(skc17,u)
| ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ m1_subset_1(skc17,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ l1_vectsp_2(skc16,skc15)
| ~ v5_vectsp_2(skc16,skc15)
| v10_vectsp_1(skc15)
| v3_struct_0(skc15)
| m1_rmod_2(skc16,skc15,k1_rmod_5(skc15,skc16,u)) ),
inference(spr,[status(thm),theory(equality)],[57,341]),
[iquote('0:SpR:57.0,341.18')] ).
cnf(7357,plain,
( ~ m1_subset_1(skc17,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ v5_vectsp_2(skc16,skc15)
| ~ l1_vectsp_2(skc16,skc15)
| v10_vectsp_1(skc15)
| v3_struct_0(skc15)
| m1_rmod_2(skc16,skc15,skc16) ),
inference(ssi,[status(thm)],[7347,10,6,8,5,11,9,7,4,3,2,1,433]),
[iquote('0:SSi:7347.10,7347.9,7347.8,7347.7,7347.6,7347.5,7347.4,7347.3,7347.2,7347.1,7347.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0')] ).
cnf(7358,plain,
m1_rmod_2(skc16,skc15,skc16),
inference(mrr,[status(thm)],[7357,45,31,32,29,28]),
[iquote('0:MRR:7357.0,7357.1,7357.2,7357.3,7357.4,45.0,31.0,32.0,29.0,28.0')] ).
cnf(7359,plain,
( ~ r1_tarski(skc17,u)
| ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ m1_subset_1(skc17,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ l1_vectsp_2(skc16,skc15)
| ~ v5_vectsp_2(skc16,skc15)
| v10_vectsp_1(skc15)
| v3_struct_0(skc15)
| m1_rmod_2(skc16,skc15,k1_rmod_5(skc15,skc16,u)) ),
inference(ssi,[status(thm)],[7348,10,6,8,5,11,9,7,4,3,2,1,433]),
[iquote('0:SSi:7348.10,7348.9,7348.8,7348.7,7348.6,7348.5,7348.4,7348.3,7348.2,7348.1,7348.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0')] ).
cnf(7360,plain,
( ~ r1_tarski(skc17,u)
| ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc16)))
| m1_rmod_2(skc16,skc15,k1_rmod_5(skc15,skc16,u)) ),
inference(mrr,[status(thm)],[7359,45,32,31,29,28]),
[iquote('0:MRR:7359.2,7359.3,7359.4,7359.5,7359.6,45.0,32.0,31.0,29.0,28.0')] ).
cnf(7372,plain,
( ~ l3_vectsp_1(skc15)
| ~ v8_vectsp_1(skc15)
| ~ v7_vectsp_1(skc15)
| ~ v6_vectsp_1(skc15)
| ~ v4_group_1(skc15)
| ~ v6_rlvect_1(skc15)
| ~ v5_rlvect_1(skc15)
| ~ v4_rlvect_1(skc15)
| ~ v3_rlvect_1(skc15)
| ~ v3_struct_0(skc16)
| ~ v5_vectsp_2(skc16,skc15)
| ~ l1_vectsp_2(skc16,skc15)
| v3_struct_0(skc15) ),
inference(res,[status(thm),theory(equality)],[7358,329]),
[iquote('0:Res:7358.0,329.12')] ).
cnf(7377,plain,
( ~ v3_struct_0(skc16)
| ~ v5_vectsp_2(skc16,skc15)
| ~ l1_vectsp_2(skc16,skc15)
| v3_struct_0(skc15) ),
inference(ssi,[status(thm)],[7372,10,6,8,5,11,9,7,4,3,2,1,433]),
[iquote('0:SSi:7372.8,7372.7,7372.6,7372.5,7372.4,7372.3,7372.2,7372.1,7372.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0')] ).
cnf(7378,plain,
~ v3_struct_0(skc16),
inference(mrr,[status(thm)],[7377,31,32,28]),
[iquote('0:MRR:7377.1,7377.2,7377.3,31.0,32.0,28.0')] ).
cnf(7559,plain,
( ~ v2_vectsp_2(skc15)
| ~ v7_group_1(skc15)
| ~ v6_rlvect_1(skc16)
| ~ v5_rlvect_1(skc16)
| ~ v4_rlvect_1(skc16)
| ~ v3_rlvect_1(skc16)
| ~ l3_vectsp_1(skc15)
| ~ v8_vectsp_1(skc15)
| ~ v7_vectsp_1(skc15)
| ~ v6_vectsp_1(skc15)
| ~ v4_group_1(skc15)
| ~ v6_rlvect_1(skc15)
| ~ v5_rlvect_1(skc15)
| ~ v4_rlvect_1(skc15)
| ~ v3_rlvect_1(skc15)
| ~ r1_tarski(skc17,u)
| ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ l1_vectsp_2(skc16,skc15)
| ~ v5_vectsp_2(skc16,skc15)
| ~ v3_vectsp_2(skc16,skc15)
| v10_vectsp_1(skc15)
| v3_struct_0(skc16)
| v3_struct_0(skc15)
| equal(k1_rmod_5(skc15,skc16,u),skc16) ),
inference(res,[status(thm),theory(equality)],[7360,1537]),
[iquote('0:Res:7360.2,1537.19')] ).
cnf(7560,plain,
( ~ v2_vectsp_2(skc15)
| ~ v7_group_1(skc15)
| ~ v6_rlvect_1(skc16)
| ~ v5_rlvect_1(skc16)
| ~ v4_rlvect_1(skc16)
| ~ v3_rlvect_1(skc16)
| ~ l3_vectsp_1(skc15)
| ~ v8_vectsp_1(skc15)
| ~ v7_vectsp_1(skc15)
| ~ v6_vectsp_1(skc15)
| ~ v4_group_1(skc15)
| ~ v6_rlvect_1(skc15)
| ~ v5_rlvect_1(skc15)
| ~ v4_rlvect_1(skc15)
| ~ v3_rlvect_1(skc15)
| ~ r1_tarski(skc17,u)
| ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ l1_vectsp_2(skc16,skc15)
| ~ v5_vectsp_2(skc16,skc15)
| ~ v3_vectsp_2(skc16,skc15)
| v10_vectsp_1(skc15)
| v3_struct_0(skc16)
| v3_struct_0(skc15)
| equal(k1_rmod_5(skc15,skc16,u),skc16) ),
inference(obv,[status(thm),theory(equality)],[7559]),
[iquote('0:Obv:7559.16')] ).
cnf(7561,plain,
( ~ r1_tarski(skc17,u)
| ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc16)))
| ~ l1_vectsp_2(skc16,skc15)
| ~ v5_vectsp_2(skc16,skc15)
| ~ v3_vectsp_2(skc16,skc15)
| v10_vectsp_1(skc15)
| v3_struct_0(skc16)
| v3_struct_0(skc15)
| equal(k1_rmod_5(skc15,skc16,u),skc16) ),
inference(ssi,[status(thm)],[7560,10,6,8,5,11,9,7,4,3,2,1,433,15,14,13,12,364]),
[iquote('0:SSi:7560.14,7560.13,7560.12,7560.11,7560.10,7560.9,7560.8,7560.7,7560.6,7560.5,7560.4,7560.3,7560.2,7560.1,7560.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,15.0,14.0,13.0,12.0,364.0,15.0,14.0,13.0,12.0,364.0,15.0,14.0,13.0,12.0,364.0,15.0,14.0,13.0,12.0,364.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0,10.0,6.0,8.0,5.0,11.0,9.0,7.0,4.0,3.0,2.0,1.0,433.0')] ).
cnf(7562,plain,
( ~ r1_tarski(skc17,u)
| ~ m1_subset_1(u,k1_zfmisc_1(u1_struct_0(skc16)))
| equal(k1_rmod_5(skc15,skc16,u),skc16) ),
inference(mrr,[status(thm)],[7561,32,31,30,29,7378,28]),
[iquote('0:MRR:7561.2,7561.3,7561.4,7561.5,7561.6,7561.7,32.0,31.0,30.0,29.0,7378.0,28.0')] ).
cnf(7760,plain,
( ~ r1_tarski(skc17,skc18)
| equal(k1_rmod_5(skc15,skc16,skc18),skc16) ),
inference(res,[status(thm),theory(equality)],[44,7562]),
[iquote('0:Res:44.0,7562.1')] ).
cnf(7765,plain,
$false,
inference(mrr,[status(thm)],[7760,33,64]),
[iquote('0:MRR:7760.0,7760.1,33.0,64.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ALG220+1 : TPTP v8.1.0. Released v3.4.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Wed Jun 8 21:59:21 EDT 2022
% 0.15/0.36 % CPUTime :
% 5.04/5.23
% 5.04/5.23 SPASS V 3.9
% 5.04/5.23 SPASS beiseite: Proof found.
% 5.04/5.23 % SZS status Theorem
% 5.04/5.23 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.04/5.23 SPASS derived 5165 clauses, backtracked 1009 clauses, performed 6 splits and kept 3539 clauses.
% 5.04/5.23 SPASS allocated 108187 KBytes.
% 5.04/5.23 SPASS spent 0:00:04.85 on the problem.
% 5.04/5.23 0:00:00.04 for the input.
% 5.04/5.23 0:00:00.09 for the FLOTTER CNF translation.
% 5.04/5.23 0:00:00.15 for inferences.
% 5.04/5.23 0:00:00.02 for the backtracking.
% 5.04/5.23 0:00:04.41 for the reduction.
% 5.04/5.23
% 5.04/5.23
% 5.04/5.23 Here is a proof with depth 4, length 72 :
% 5.04/5.23 % SZS output start Refutation
% See solution above
% 5.10/5.35 Formulae used in the proof : t16_rmod_5 dt_l2_struct_0 dt_l2_vectsp_1 dt_l3_vectsp_1 dt_l1_vectsp_2 cc3_vectsp_2 dt_m1_rmod_2 dt_k1_rmod_5 t15_rmod_5 t33_rmod_2
% 5.10/5.35
%------------------------------------------------------------------------------