%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG216+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 18:03:01 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 28
% Syntax : Number of clauses : 43 ( 25 unt; 9 nHn; 43 RR)
% Number of literals : 190 ( 0 equ; 132 neg)
% Maximal clause size : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v3_rlvect_1(skc14),
file('ALG216+1.p',unknown),
[] ).
cnf(2,axiom,
v4_rlvect_1(skc14),
file('ALG216+1.p',unknown),
[] ).
cnf(3,axiom,
v5_rlvect_1(skc14),
file('ALG216+1.p',unknown),
[] ).
cnf(4,axiom,
v6_rlvect_1(skc14),
file('ALG216+1.p',unknown),
[] ).
cnf(5,axiom,
v4_group_1(skc14),
file('ALG216+1.p',unknown),
[] ).
cnf(6,axiom,
v6_vectsp_1(skc14),
file('ALG216+1.p',unknown),
[] ).
cnf(7,axiom,
v7_vectsp_1(skc14),
file('ALG216+1.p',unknown),
[] ).
cnf(8,axiom,
v8_vectsp_1(skc14),
file('ALG216+1.p',unknown),
[] ).
cnf(9,axiom,
l3_vectsp_1(skc14),
file('ALG216+1.p',unknown),
[] ).
cnf(10,axiom,
v3_rlvect_1(skc15),
file('ALG216+1.p',unknown),
[] ).
cnf(11,axiom,
v4_rlvect_1(skc15),
file('ALG216+1.p',unknown),
[] ).
cnf(12,axiom,
v5_rlvect_1(skc15),
file('ALG216+1.p',unknown),
[] ).
cnf(13,axiom,
v6_rlvect_1(skc15),
file('ALG216+1.p',unknown),
[] ).
cnf(25,axiom,
~ v3_struct_0(skc15),
file('ALG216+1.p',unknown),
[] ).
cnf(26,axiom,
~ v3_struct_0(skc14),
file('ALG216+1.p',unknown),
[] ).
cnf(27,axiom,
v5_vectsp_2(skc15,skc14),
file('ALG216+1.p',unknown),
[] ).
cnf(28,axiom,
l1_vectsp_2(skc15,skc14),
file('ALG216+1.p',unknown),
[] ).
cnf(34,axiom,
m1_subset_1(skc16,u1_struct_0(skc15)),
file('ALG216+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ l1_rlvect_1(u)
| l2_struct_0(u) ),
file('ALG216+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ l2_struct_0(u)
| l1_struct_0(u) ),
file('ALG216+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ l3_vectsp_1(u)
| l1_rlvect_1(u) ),
file('ALG216+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ l3_vectsp_1(u)
| l2_vectsp_1(u) ),
file('ALG216+1.p',unknown),
[] ).
cnf(49,axiom,
~ equal(k2_group_1(skc14),k1_rlvect_1(skc14)),
file('ALG216+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ l2_struct_0(u)
| m1_subset_1(k1_rlvect_1(u),u1_struct_0(u)) ),
file('ALG216+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ l1_struct_0(u)
| ~ l1_vectsp_2(v,u)
| l1_rlvect_1(v) ),
file('ALG216+1.p',unknown),
[] ).
cnf(73,axiom,
( v1_rmod_5(k8_rlvect_2(skc15,skc16,k1_rlvect_1(skc15)),skc14,skc15)
| v1_rmod_5(k8_rlvect_2(skc15,k1_rlvect_1(skc15),skc16),skc14,skc15) ),
file('ALG216+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ 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)
| ~ m1_subset_1(w,u1_struct_0(u))
| ~ m1_subset_1(x,u1_struct_0(u))
| ~ equal(w,k1_rlvect_1(u))
| ~ v1_rmod_5(k8_rlvect_2(u,x,w),v,u)
| v3_struct_0(u)
| v3_struct_0(v)
| equal(k2_group_1(v),k1_rlvect_1(v)) ),
file('ALG216+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ 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)
| ~ m1_subset_1(w,u1_struct_0(u))
| ~ m1_subset_1(x,u1_struct_0(u))
| ~ equal(x,k1_rlvect_1(u))
| ~ v1_rmod_5(k8_rlvect_2(u,x,w),v,u)
| v3_struct_0(u)
| v3_struct_0(v)
| equal(k2_group_1(v),k1_rlvect_1(v)) ),
file('ALG216+1.p',unknown),
[] ).
cnf(101,plain,
l1_rlvect_1(skc14),
inference(res,[status(thm),theory(equality)],[9,47]),
[iquote('0:Res:9.0,47.0')] ).
cnf(102,plain,
l2_vectsp_1(skc14),
inference(res,[status(thm),theory(equality)],[9,48]),
[iquote('0:Res:9.0,48.0')] ).
cnf(129,plain,
( ~ l1_struct_0(skc14)
| l1_rlvect_1(skc15) ),
inference(res,[status(thm),theory(equality)],[28,69]),
[iquote('0:Res:28.0,69.1')] ).
cnf(187,plain,
( ~ l2_struct_0(skc14)
| l1_rlvect_1(skc15) ),
inference(sor,[status(thm)],[129,43]),
[iquote('0:SoR:129.0,43.1')] ).
cnf(188,plain,
l1_rlvect_1(skc15),
inference(ssi,[status(thm)],[187,42,8,7,6,5,9,4,3,2,1,102,101]),
[iquote('0:SSi:187.0,42.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.1')] ).
cnf(378,plain,
( ~ v6_rlvect_1(skc15)
| ~ v5_rlvect_1(skc15)
| ~ v4_rlvect_1(skc15)
| ~ v3_rlvect_1(skc15)
| ~ l3_vectsp_1(skc14)
| ~ v8_vectsp_1(skc14)
| ~ v7_vectsp_1(skc14)
| ~ v6_vectsp_1(skc14)
| ~ v4_group_1(skc14)
| ~ v6_rlvect_1(skc14)
| ~ v5_rlvect_1(skc14)
| ~ v4_rlvect_1(skc14)
| ~ v3_rlvect_1(skc14)
| ~ l1_vectsp_2(skc15,skc14)
| ~ v5_vectsp_2(skc15,skc14)
| ~ m1_subset_1(skc16,u1_struct_0(skc15))
| ~ m1_subset_1(k1_rlvect_1(skc15),u1_struct_0(skc15))
| ~ equal(k1_rlvect_1(skc15),k1_rlvect_1(skc15))
| v1_rmod_5(k8_rlvect_2(skc15,skc16,k1_rlvect_1(skc15)),skc14,skc15)
| v3_struct_0(skc15)
| v3_struct_0(skc14)
| equal(k2_group_1(skc14),k1_rlvect_1(skc14)) ),
inference(res,[status(thm),theory(equality)],[73,79]),
[iquote('0:Res:73.1,79.18')] ).
cnf(379,plain,
( ~ v6_rlvect_1(skc15)
| ~ v5_rlvect_1(skc15)
| ~ v4_rlvect_1(skc15)
| ~ v3_rlvect_1(skc15)
| ~ l3_vectsp_1(skc14)
| ~ v8_vectsp_1(skc14)
| ~ v7_vectsp_1(skc14)
| ~ v6_vectsp_1(skc14)
| ~ v4_group_1(skc14)
| ~ v6_rlvect_1(skc14)
| ~ v5_rlvect_1(skc14)
| ~ v4_rlvect_1(skc14)
| ~ v3_rlvect_1(skc14)
| ~ l1_vectsp_2(skc15,skc14)
| ~ v5_vectsp_2(skc15,skc14)
| ~ m1_subset_1(skc16,u1_struct_0(skc15))
| ~ m1_subset_1(k1_rlvect_1(skc15),u1_struct_0(skc15))
| v1_rmod_5(k8_rlvect_2(skc15,skc16,k1_rlvect_1(skc15)),skc14,skc15)
| v3_struct_0(skc15)
| v3_struct_0(skc14)
| equal(k2_group_1(skc14),k1_rlvect_1(skc14)) ),
inference(obv,[status(thm),theory(equality)],[378]),
[iquote('0:Obv:378.17')] ).
cnf(380,plain,
( ~ l1_vectsp_2(skc15,skc14)
| ~ v5_vectsp_2(skc15,skc14)
| ~ m1_subset_1(skc16,u1_struct_0(skc15))
| ~ m1_subset_1(k1_rlvect_1(skc15),u1_struct_0(skc15))
| v1_rmod_5(k8_rlvect_2(skc15,skc16,k1_rlvect_1(skc15)),skc14,skc15)
| v3_struct_0(skc15)
| v3_struct_0(skc14)
| equal(k2_group_1(skc14),k1_rlvect_1(skc14)) ),
inference(ssi,[status(thm)],[379,8,7,6,5,9,4,3,2,1,102,101,13,12,11,10,188]),
[iquote('0:SSi:379.12,379.11,379.10,379.9,379.8,379.7,379.6,379.5,379.4,379.3,379.2,379.1,379.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,13.0,12.0,11.0,10.0,188.0,13.0,12.0,11.0,10.0,188.0,13.0,12.0,11.0,10.0,188.0,13.0,12.0,11.0,10.0,188.0')] ).
cnf(381,plain,
( ~ m1_subset_1(k1_rlvect_1(skc15),u1_struct_0(skc15))
| v1_rmod_5(k8_rlvect_2(skc15,skc16,k1_rlvect_1(skc15)),skc14,skc15) ),
inference(mrr,[status(thm)],[380,28,27,34,25,26,49]),
[iquote('0:MRR:380.0,380.1,380.2,380.5,380.6,380.7,28.0,27.0,34.0,25.0,26.0,49.0')] ).
cnf(454,plain,
( ~ v6_rlvect_1(skc15)
| ~ v5_rlvect_1(skc15)
| ~ v4_rlvect_1(skc15)
| ~ v3_rlvect_1(skc15)
| ~ l3_vectsp_1(skc14)
| ~ v8_vectsp_1(skc14)
| ~ v7_vectsp_1(skc14)
| ~ v6_vectsp_1(skc14)
| ~ v4_group_1(skc14)
| ~ v6_rlvect_1(skc14)
| ~ v5_rlvect_1(skc14)
| ~ v4_rlvect_1(skc14)
| ~ v3_rlvect_1(skc14)
| ~ m1_subset_1(k1_rlvect_1(skc15),u1_struct_0(skc15))
| ~ l1_vectsp_2(skc15,skc14)
| ~ v5_vectsp_2(skc15,skc14)
| ~ m1_subset_1(k1_rlvect_1(skc15),u1_struct_0(skc15))
| ~ m1_subset_1(skc16,u1_struct_0(skc15))
| ~ equal(k1_rlvect_1(skc15),k1_rlvect_1(skc15))
| v3_struct_0(skc15)
| v3_struct_0(skc14)
| equal(k2_group_1(skc14),k1_rlvect_1(skc14)) ),
inference(res,[status(thm),theory(equality)],[381,78]),
[iquote('0:Res:381.1,78.18')] ).
cnf(460,plain,
( ~ v6_rlvect_1(skc15)
| ~ v5_rlvect_1(skc15)
| ~ v4_rlvect_1(skc15)
| ~ v3_rlvect_1(skc15)
| ~ l3_vectsp_1(skc14)
| ~ v8_vectsp_1(skc14)
| ~ v7_vectsp_1(skc14)
| ~ v6_vectsp_1(skc14)
| ~ v4_group_1(skc14)
| ~ v6_rlvect_1(skc14)
| ~ v5_rlvect_1(skc14)
| ~ v4_rlvect_1(skc14)
| ~ v3_rlvect_1(skc14)
| ~ l1_vectsp_2(skc15,skc14)
| ~ v5_vectsp_2(skc15,skc14)
| ~ m1_subset_1(k1_rlvect_1(skc15),u1_struct_0(skc15))
| ~ m1_subset_1(skc16,u1_struct_0(skc15))
| v3_struct_0(skc15)
| v3_struct_0(skc14)
| equal(k2_group_1(skc14),k1_rlvect_1(skc14)) ),
inference(obv,[status(thm),theory(equality)],[454]),
[iquote('0:Obv:454.18')] ).
cnf(461,plain,
( ~ l1_vectsp_2(skc15,skc14)
| ~ v5_vectsp_2(skc15,skc14)
| ~ m1_subset_1(k1_rlvect_1(skc15),u1_struct_0(skc15))
| ~ m1_subset_1(skc16,u1_struct_0(skc15))
| v3_struct_0(skc15)
| v3_struct_0(skc14)
| equal(k2_group_1(skc14),k1_rlvect_1(skc14)) ),
inference(ssi,[status(thm)],[460,8,7,6,5,9,4,3,2,1,102,101,13,12,11,10,188]),
[iquote('0:SSi:460.12,460.11,460.10,460.9,460.8,460.7,460.6,460.5,460.4,460.3,460.2,460.1,460.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,8.0,7.0,6.0,5.0,9.0,4.0,3.0,2.0,1.0,102.0,101.0,13.0,12.0,11.0,10.0,188.0,13.0,12.0,11.0,10.0,188.0,13.0,12.0,11.0,10.0,188.0,13.0,12.0,11.0,10.0,188.0')] ).
cnf(462,plain,
~ m1_subset_1(k1_rlvect_1(skc15),u1_struct_0(skc15)),
inference(mrr,[status(thm)],[461,28,27,34,25,26,49]),
[iquote('0:MRR:461.0,461.1,461.3,461.4,461.5,461.6,28.0,27.0,34.0,25.0,26.0,49.0')] ).
cnf(463,plain,
~ l2_struct_0(skc15),
inference(res,[status(thm),theory(equality)],[63,462]),
[iquote('0:Res:63.1,462.0')] ).
cnf(464,plain,
$false,
inference(ssi,[status(thm)],[463,42,13,12,11,10,188]),
[iquote('0:SSi:463.0,42.0,13.0,12.0,11.0,10.0,188.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG216+1 : TPTP v8.1.0. Released v3.4.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 06:30:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.51
% 0.19/0.51 SPASS V 3.9
% 0.19/0.51 SPASS beiseite: Proof found.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 294 clauses, backtracked 0 clauses, performed 0 splits and kept 240 clauses.
% 0.19/0.51 SPASS allocated 98245 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.15 on the problem.
% 0.19/0.51 0:00:00.04 for the input.
% 0.19/0.51 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.51 0:00:00.00 for inferences.
% 0.19/0.51 0:00:00.00 for the backtracking.
% 0.19/0.51 0:00:00.02 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 3, length 43 :
% 0.19/0.51 % SZS output start Refutation
% See solution above
% 0.19/0.51 Formulae used in the proof : t6_rmod_5 dt_l1_rlvect_1 dt_l2_struct_0 dt_l3_vectsp_1 dt_k1_rlvect_1 dt_l1_vectsp_2 t5_rmod_5
% 0.19/0.51
%------------------------------------------------------------------------------