TSTP Solution File: SEU411+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU411+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 : Tue Jul 19 14:37:04 EDT 2022
% Result : Theorem 65.22s 65.42s
% Output : Refutation 65.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 34
% Syntax : Number of clauses : 75 ( 30 unt; 19 nHn; 75 RR)
% Number of literals : 180 ( 0 equ; 90 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v2_orders_2(skc7),
file('SEU411+1.p',unknown),
[] ).
cnf(2,axiom,
v3_orders_2(skc7),
file('SEU411+1.p',unknown),
[] ).
cnf(3,axiom,
v4_orders_2(skc7),
file('SEU411+1.p',unknown),
[] ).
cnf(4,axiom,
v1_yellow_0(skc7),
file('SEU411+1.p',unknown),
[] ).
cnf(5,axiom,
v1_lattice3(skc7),
file('SEU411+1.p',unknown),
[] ).
cnf(6,axiom,
l1_orders_2(skc7),
file('SEU411+1.p',unknown),
[] ).
cnf(7,axiom,
v2_orders_2(skc8),
file('SEU411+1.p',unknown),
[] ).
cnf(8,axiom,
v3_orders_2(skc8),
file('SEU411+1.p',unknown),
[] ).
cnf(9,axiom,
v4_orders_2(skc8),
file('SEU411+1.p',unknown),
[] ).
cnf(10,axiom,
v1_yellow_0(skc8),
file('SEU411+1.p',unknown),
[] ).
cnf(11,axiom,
v1_lattice3(skc8),
file('SEU411+1.p',unknown),
[] ).
cnf(12,axiom,
l1_orders_2(skc8),
file('SEU411+1.p',unknown),
[] ).
cnf(18,axiom,
~ v3_struct_0(skc8),
file('SEU411+1.p',unknown),
[] ).
cnf(19,axiom,
~ v3_struct_0(skc7),
file('SEU411+1.p',unknown),
[] ).
cnf(23,axiom,
m1_subset_1(skf11(u),u),
file('SEU411+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ l1_orders_2(u)
| l1_struct_0(u) ),
file('SEU411+1.p',unknown),
[] ).
cnf(25,axiom,
equal(k3_xboole_0(u,u),u),
file('SEU411+1.p',unknown),
[] ).
cnf(27,axiom,
~ r2_hidden(k3_yellow_0(skc8),u1_struct_0(skc7)),
file('SEU411+1.p',unknown),
[] ).
cnf(33,axiom,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8))),
file('SEU411+1.p',unknown),
[] ).
cnf(35,axiom,
v12_waybel_0(k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)),skc8),
file('SEU411+1.p',unknown),
[] ).
cnf(36,axiom,
equal(k3_xboole_0(u,v),k3_xboole_0(v,u)),
file('SEU411+1.p',unknown),
[] ).
cnf(37,axiom,
( equal(u,k1_xboole_0)
| r2_hidden(skf9(u),u) ),
file('SEU411+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ r2_hidden(u,v)
| ~ equal(v,k1_xboole_0) ),
file('SEU411+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ l1_orders_2(u)
| m1_subset_1(k3_yellow_0(u),u1_struct_0(u)) ),
file('SEU411+1.p',unknown),
[] ).
cnf(45,axiom,
m1_subset_1(k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)),k1_zfmisc_1(u1_struct_0(skc8))),
file('SEU411+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ l1_struct_0(u)
| ~ v1_xboole_0(u1_struct_0(u))
| v3_struct_0(u) ),
file('SEU411+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ m1_subset_1(u,v)
| v1_xboole_0(v)
| r2_hidden(u,v) ),
file('SEU411+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ r2_hidden(u,v)
| ~ m1_subset_1(v,k1_zfmisc_1(w))
| m1_subset_1(u,w) ),
file('SEU411+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ r2_hidden(u,v)
| ~ equal(v,k3_xboole_0(w,x))
| r2_hidden(u,x) ),
file('SEU411+1.p',unknown),
[] ).
cnf(60,axiom,
( equal(u,k3_xboole_0(v,w))
| r2_hidden(skf10(w,v,u),u)
| r2_hidden(skf10(w,v,u),w) ),
file('SEU411+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ l1_orders_2(u)
| ~ v1_yellow_0(u)
| ~ v4_orders_2(u)
| ~ m1_subset_1(v,u1_struct_0(u))
| v3_struct_0(u)
| r1_orders_2(u,k3_yellow_0(u),v) ),
file('SEU411+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ l1_orders_2(u)
| ~ l1_orders_2(v)
| ~ r2_hidden(w,k3_xboole_0(u1_struct_0(v),u1_struct_0(u)))
| v3_struct_0(u)
| v3_struct_0(v)
| m1_subset_1(w,u1_struct_0(u)) ),
file('SEU411+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ r2_hidden(skf10(u,v,w),u)
| ~ r2_hidden(skf10(u,v,w),v)
| ~ r2_hidden(skf10(u,v,w),w)
| equal(w,k3_xboole_0(v,u)) ),
file('SEU411+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ l1_orders_2(u)
| ~ m1_subset_1(v,u1_struct_0(u))
| ~ m1_subset_1(w,u1_struct_0(u))
| ~ r1_orders_2(u,w,v)
| ~ r2_hidden(v,x)
| ~ v12_waybel_0(x,u)
| ~ m1_subset_1(x,k1_zfmisc_1(u1_struct_0(u)))
| r2_hidden(w,x) ),
file('SEU411+1.p',unknown),
[] ).
cnf(70,plain,
( ~ l1_orders_2(u)
| ~ v12_waybel_0(v,u)
| ~ r2_hidden(w,v)
| ~ m1_subset_1(x,u1_struct_0(u))
| ~ m1_subset_1(v,k1_zfmisc_1(u1_struct_0(u)))
| ~ r1_orders_2(u,x,w)
| r2_hidden(x,v) ),
inference(mrr,[status(thm)],[69,50]),
[iquote('0:MRR:69.1,50.2')] ).
cnf(75,plain,
( ~ v4_orders_2(skc8)
| ~ v1_yellow_0(skc8)
| ~ m1_subset_1(u,u1_struct_0(skc8))
| v3_struct_0(skc8)
| r1_orders_2(skc8,k3_yellow_0(skc8),u) ),
inference(res,[status(thm),theory(equality)],[12,64]),
[iquote('0:Res:12.0,64.2')] ).
cnf(83,plain,
m1_subset_1(k3_yellow_0(skc8),u1_struct_0(skc8)),
inference(res,[status(thm),theory(equality)],[12,42]),
[iquote('0:Res:12.0,42.0')] ).
cnf(84,plain,
l1_struct_0(skc8),
inference(res,[status(thm),theory(equality)],[12,24]),
[iquote('0:Res:12.0,24.0')] ).
cnf(110,plain,
l1_struct_0(skc7),
inference(res,[status(thm),theory(equality)],[6,24]),
[iquote('0:Res:6.0,24.0')] ).
cnf(131,plain,
( ~ l1_struct_0(skc7)
| ~ v1_xboole_0(u1_struct_0(skc7)) ),
inference(res,[status(thm),theory(equality)],[46,19]),
[iquote('0:Res:46.2,19.0')] ).
cnf(145,plain,
~ v1_xboole_0(u1_struct_0(skc7)),
inference(mrr,[status(thm)],[131,110]),
[iquote('0:MRR:131.0,110.0')] ).
cnf(157,plain,
( ~ m1_subset_1(u,u1_struct_0(skc8))
| r1_orders_2(skc8,k3_yellow_0(skc8),u) ),
inference(mrr,[status(thm)],[75,9,10,18]),
[iquote('0:MRR:75.0,75.1,75.3,9.0,10.0,18.0')] ).
cnf(198,plain,
( ~ m1_subset_1(k3_yellow_0(skc8),u1_struct_0(skc7))
| v1_xboole_0(u1_struct_0(skc7)) ),
inference(res,[status(thm),theory(equality)],[48,27]),
[iquote('0:Res:48.2,27.0')] ).
cnf(201,plain,
( ~ m1_subset_1(u,v)
| ~ equal(v,k1_xboole_0)
| v1_xboole_0(v) ),
inference(res,[status(thm),theory(equality)],[48,41]),
[iquote('0:Res:48.2,41.0')] ).
cnf(204,plain,
~ m1_subset_1(k3_yellow_0(skc8),u1_struct_0(skc7)),
inference(mrr,[status(thm)],[198,145]),
[iquote('0:MRR:198.1,145.0')] ).
cnf(222,plain,
( ~ r2_hidden(u,k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)))
| m1_subset_1(u,u1_struct_0(skc8)) ),
inference(res,[status(thm),theory(equality)],[45,50]),
[iquote('0:Res:45.0,50.1')] ).
cnf(231,plain,
( ~ r2_hidden(u,k3_xboole_0(v,w))
| r2_hidden(u,w) ),
inference(eqr,[status(thm),theory(equality)],[53]),
[iquote('0:EqR:53.1')] ).
cnf(233,plain,
( ~ r2_hidden(u,v)
| ~ equal(v,w)
| r2_hidden(u,w) ),
inference(spl,[status(thm),theory(equality)],[25,53]),
[iquote('0:SpL:25.0,53.1')] ).
cnf(255,plain,
( equal(k3_xboole_0(u,v),k1_xboole_0)
| r2_hidden(skf9(k3_xboole_0(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[37,231]),
[iquote('0:Res:37.1,231.0')] ).
cnf(264,plain,
( ~ equal(u,k1_xboole_0)
| v1_xboole_0(u) ),
inference(res,[status(thm),theory(equality)],[23,201]),
[iquote('0:Res:23.0,201.0')] ).
cnf(293,plain,
~ equal(k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)),k1_xboole_0),
inference(res,[status(thm),theory(equality)],[264,33]),
[iquote('0:Res:264.1,33.0')] ).
cnf(369,plain,
( equal(k3_xboole_0(u,v),v)
| r2_hidden(skf10(v,u,v),v) ),
inference(fac,[status(thm)],[60]),
[iquote('0:Fac:60.1,60.2')] ).
cnf(467,plain,
( equal(k3_xboole_0(u,v),k1_xboole_0)
| r2_hidden(skf9(k3_xboole_0(v,u)),v) ),
inference(spr,[status(thm),theory(equality)],[36,255]),
[iquote('0:SpR:36.0,255.1')] ).
cnf(608,plain,
( ~ l1_orders_2(u)
| ~ l1_orders_2(v)
| ~ r2_hidden(w,k3_xboole_0(u1_struct_0(u),u1_struct_0(v)))
| v3_struct_0(u)
| v3_struct_0(v)
| m1_subset_1(w,u1_struct_0(u)) ),
inference(spl,[status(thm),theory(equality)],[36,65]),
[iquote('0:SpL:36.0,65.2')] ).
cnf(822,plain,
( ~ l1_orders_2(skc8)
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)),skc8)
| ~ r2_hidden(u,k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)))
| ~ m1_subset_1(v,u1_struct_0(skc8))
| ~ r1_orders_2(skc8,v,u)
| r2_hidden(v,k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8))) ),
inference(res,[status(thm),theory(equality)],[45,70]),
[iquote('0:Res:45.0,70.4')] ).
cnf(828,plain,
( ~ v12_waybel_0(k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)),skc8)
| ~ r2_hidden(u,k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)))
| ~ m1_subset_1(v,u1_struct_0(skc8))
| ~ r1_orders_2(skc8,v,u)
| r2_hidden(v,k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8))) ),
inference(ssi,[status(thm)],[822,11,10,9,8,7,12,84]),
[iquote('0:SSi:822.0,11.0,10.0,9.0,8.0,7.0,12.0,84.0')] ).
cnf(829,plain,
( ~ r2_hidden(u,k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)))
| ~ m1_subset_1(v,u1_struct_0(skc8))
| ~ r1_orders_2(skc8,v,u)
| r2_hidden(v,k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8))) ),
inference(mrr,[status(thm)],[828,35]),
[iquote('0:MRR:828.0,35.0')] ).
cnf(838,plain,
( ~ r2_hidden(skf10(u,v,u),v)
| ~ r2_hidden(skf10(u,v,u),u)
| equal(k3_xboole_0(v,u),u)
| equal(k3_xboole_0(v,u),u) ),
inference(res,[status(thm),theory(equality)],[369,66]),
[iquote('0:Res:369.1,66.0')] ).
cnf(839,plain,
( ~ equal(u,v)
| equal(k3_xboole_0(w,u),u)
| r2_hidden(skf10(u,w,u),v) ),
inference(res,[status(thm),theory(equality)],[369,233]),
[iquote('0:Res:369.1,233.0')] ).
cnf(852,plain,
( ~ r2_hidden(skf10(u,v,u),v)
| ~ r2_hidden(skf10(u,v,u),u)
| equal(k3_xboole_0(v,u),u) ),
inference(obv,[status(thm),theory(equality)],[838]),
[iquote('0:Obv:838.2')] ).
cnf(853,plain,
( ~ r2_hidden(skf10(u,v,u),v)
| equal(k3_xboole_0(v,u),u) ),
inference(mrr,[status(thm)],[852,369]),
[iquote('0:MRR:852.1,369.1')] ).
cnf(3929,plain,
( ~ m1_subset_1(u,u1_struct_0(skc8))
| ~ r1_orders_2(skc8,u,skf9(k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8))))
| equal(k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)),k1_xboole_0)
| r2_hidden(u,k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8))) ),
inference(res,[status(thm),theory(equality)],[37,829]),
[iquote('0:Res:37.1,829.0')] ).
cnf(3979,plain,
( ~ m1_subset_1(u,u1_struct_0(skc8))
| ~ r1_orders_2(skc8,u,skf9(k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8))))
| r2_hidden(u,k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8))) ),
inference(mrr,[status(thm)],[3929,293]),
[iquote('0:MRR:3929.2,293.0')] ).
cnf(8105,plain,
( ~ equal(u,v)
| equal(k3_xboole_0(v,u),u)
| equal(k3_xboole_0(v,u),u) ),
inference(res,[status(thm),theory(equality)],[839,853]),
[iquote('0:Res:839.2,853.0')] ).
cnf(8111,plain,
( ~ equal(u,v)
| equal(k3_xboole_0(v,u),u) ),
inference(obv,[status(thm),theory(equality)],[8105]),
[iquote('0:Obv:8105.1')] ).
cnf(8171,plain,
( ~ equal(u,v)
| equal(k3_xboole_0(u,v),k1_xboole_0)
| r2_hidden(skf9(u),v) ),
inference(spr,[status(thm),theory(equality)],[8111,467]),
[iquote('0:SpR:8111.1,467.1')] ).
cnf(8289,plain,
( ~ equal(u,v)
| equal(v,k1_xboole_0)
| r2_hidden(skf9(u),v) ),
inference(rew,[status(thm),theory(equality)],[8111,8171]),
[iquote('0:Rew:8111.1,8171.1')] ).
cnf(8740,plain,
( ~ equal(u,k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)))
| equal(k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)),k1_xboole_0)
| m1_subset_1(skf9(u),u1_struct_0(skc8)) ),
inference(res,[status(thm),theory(equality)],[8289,222]),
[iquote('0:Res:8289.2,222.0')] ).
cnf(8786,plain,
( ~ equal(u,k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8)))
| m1_subset_1(skf9(u),u1_struct_0(skc8)) ),
inference(mrr,[status(thm)],[8740,293]),
[iquote('0:MRR:8740.1,293.0')] ).
cnf(10578,plain,
m1_subset_1(skf9(k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8))),u1_struct_0(skc8)),
inference(eqr,[status(thm),theory(equality)],[8786]),
[iquote('0:EqR:8786.0')] ).
cnf(35044,plain,
( ~ m1_subset_1(skf9(k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8))),u1_struct_0(skc8))
| ~ m1_subset_1(k3_yellow_0(skc8),u1_struct_0(skc8))
| r2_hidden(k3_yellow_0(skc8),k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8))) ),
inference(res,[status(thm),theory(equality)],[157,3979]),
[iquote('0:Res:157.1,3979.1')] ).
cnf(35048,plain,
r2_hidden(k3_yellow_0(skc8),k3_xboole_0(u1_struct_0(skc7),u1_struct_0(skc8))),
inference(mrr,[status(thm)],[35044,10578,83]),
[iquote('0:MRR:35044.0,35044.1,10578.0,83.0')] ).
cnf(35084,plain,
( ~ l1_orders_2(skc7)
| ~ l1_orders_2(skc8)
| v3_struct_0(skc7)
| v3_struct_0(skc8)
| m1_subset_1(k3_yellow_0(skc8),u1_struct_0(skc7)) ),
inference(res,[status(thm),theory(equality)],[35048,608]),
[iquote('0:Res:35048.0,608.2')] ).
cnf(35090,plain,
( v3_struct_0(skc7)
| v3_struct_0(skc8)
| m1_subset_1(k3_yellow_0(skc8),u1_struct_0(skc7)) ),
inference(ssi,[status(thm)],[35084,11,10,9,8,7,12,84,5,4,3,2,1,6,110]),
[iquote('0:SSi:35084.1,35084.0,11.0,10.0,9.0,8.0,7.0,12.0,84.0,5.0,4.0,3.0,2.0,1.0,6.0,110.0')] ).
cnf(35091,plain,
$false,
inference(mrr,[status(thm)],[35090,19,18,204]),
[iquote('0:MRR:35090.0,35090.1,35090.2,19.0,18.0,204.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU411+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 00:52:40 EDT 2022
% 0.13/0.33 % CPUTime :
% 65.22/65.42
% 65.22/65.42 SPASS V 3.9
% 65.22/65.42 SPASS beiseite: Proof found.
% 65.22/65.42 % SZS status Theorem
% 65.22/65.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 65.22/65.42 SPASS derived 30436 clauses, backtracked 0 clauses, performed 17 splits and kept 15408 clauses.
% 65.22/65.42 SPASS allocated 125515 KBytes.
% 65.22/65.42 SPASS spent 0:01:05.05 on the problem.
% 65.22/65.42 0:00:00.04 for the input.
% 65.22/65.42 0:00:00.04 for the FLOTTER CNF translation.
% 65.22/65.42 0:00:00.45 for inferences.
% 65.22/65.42 0:00:00.27 for the backtracking.
% 65.22/65.42 0:01:03.84 for the reduction.
% 65.22/65.42
% 65.22/65.42
% 65.22/65.42 Here is a proof with depth 6, length 75 :
% 65.22/65.42 % SZS output start Refutation
% See solution above
% 65.22/65.42 Formulae used in the proof : t20_latsum_1 existence_m1_subset_1 dt_l1_orders_2 idempotence_k3_xboole_0 commutativity_k3_xboole_0 d1_xboole_0 dt_k3_yellow_0 fc1_struct_0 t2_subset t4_subset d3_xboole_0 t44_yellow_0 t13_latsum_1 d19_waybel_0
% 66.03/66.18
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