TSTP Solution File: SEU360+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU360+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 14:36:36 EDT 2022
% Result : Theorem 0.38s 0.55s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of clauses : 62 ( 16 unt; 13 nHn; 62 RR)
% Number of literals : 176 ( 0 equ; 106 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
antisymmetric_relstr(skc7),
file('SEU360+1.p',unknown),
[] ).
cnf(2,axiom,
lower_bounded_relstr(skc7),
file('SEU360+1.p',unknown),
[] ).
cnf(3,axiom,
rel_str(skc7),
file('SEU360+1.p',unknown),
[] ).
cnf(10,axiom,
~ empty_carrier(skc7),
file('SEU360+1.p',unknown),
[] ).
cnf(16,axiom,
element(skf7(u),the_carrier(u)),
file('SEU360+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ rel_str(u)
| one_sorted_str(u) ),
file('SEU360+1.p',unknown),
[] ).
cnf(21,axiom,
element(skf8(u,v,w),the_carrier(w)),
file('SEU360+1.p',unknown),
[] ).
cnf(22,axiom,
element(skf11(u,v,w),the_carrier(w)),
file('SEU360+1.p',unknown),
[] ).
cnf(23,axiom,
element(skf13(u,v,w),the_carrier(w)),
file('SEU360+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ in(u,v)
| element(u,v) ),
file('SEU360+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ ex_sup_of_relstr_set(skc7,empty_set)
| ~ ex_inf_of_relstr_set(skc7,the_carrier(skc7)) ),
file('SEU360+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ one_sorted_str(u)
| ~ empty(the_carrier(u))
| empty_carrier(u) ),
file('SEU360+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ element(u,v)
| empty(v)
| in(u,v) ),
file('SEU360+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ rel_str(u)
| ~ lower_bounded_relstr(u)
| relstr_element_smaller(u,the_carrier(u),skf7(u)) ),
file('SEU360+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ rel_str(u)
| ~ element(v,the_carrier(u))
| relstr_set_smaller(u,empty_set,v) ),
file('SEU360+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ rel_str(u)
| ~ element(v,the_carrier(u))
| ~ related(u,v,skf8(v,w,u))
| relstr_element_smaller(u,w,v) ),
file('SEU360+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ rel_str(u)
| ~ antisymmetric_relstr(u)
| ~ element(v,the_carrier(u))
| ~ relstr_element_smaller(u,w,v)
| ex_inf_of_relstr_set(u,w)
| relstr_element_smaller(u,w,skf13(v,w,u)) ),
file('SEU360+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ rel_str(u)
| ~ in(v,w)
| ~ element(x,the_carrier(u))
| ~ element(v,the_carrier(u))
| ~ relstr_element_smaller(u,w,x)
| related(u,x,v) ),
file('SEU360+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ rel_str(u)
| ~ antisymmetric_relstr(u)
| ~ element(v,the_carrier(u))
| ~ relstr_element_smaller(u,w,v)
| ~ related(u,skf13(v,w,u),v)
| ex_inf_of_relstr_set(u,w) ),
file('SEU360+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ rel_str(u)
| ~ antisymmetric_relstr(u)
| ~ element(v,the_carrier(u))
| ~ relstr_set_smaller(u,w,v)
| ~ related(u,v,skf11(v,w,u))
| ex_sup_of_relstr_set(u,w) ),
file('SEU360+1.p',unknown),
[] ).
cnf(48,plain,
( ~ in(u,v)
| ~ element(w,the_carrier(skc7))
| ~ element(u,the_carrier(skc7))
| ~ relstr_element_smaller(skc7,v,w)
| related(skc7,w,u) ),
inference(res,[status(thm),theory(equality)],[3,43]),
[iquote('0:Res:3.0,43.0')] ).
cnf(53,plain,
( ~ element(u,the_carrier(skc7))
| ~ related(skc7,u,skf8(u,v,skc7))
| relstr_element_smaller(skc7,v,u) ),
inference(res,[status(thm),theory(equality)],[3,38]),
[iquote('0:Res:3.0,38.0')] ).
cnf(58,plain,
( ~ lower_bounded_relstr(skc7)
| relstr_element_smaller(skc7,the_carrier(skc7),skf7(skc7)) ),
inference(res,[status(thm),theory(equality)],[3,31]),
[iquote('0:Res:3.0,31.1')] ).
cnf(59,plain,
( ~ element(u,the_carrier(skc7))
| relstr_set_smaller(skc7,empty_set,u) ),
inference(res,[status(thm),theory(equality)],[3,32]),
[iquote('0:Res:3.0,32.0')] ).
cnf(61,plain,
one_sorted_str(skc7),
inference(res,[status(thm),theory(equality)],[3,17]),
[iquote('0:Res:3.0,17.0')] ).
cnf(63,plain,
( ~ rel_str(skc7)
| ~ relstr_set_smaller(skc7,u,v)
| ~ related(skc7,v,skf11(v,u,skc7))
| ~ element(v,the_carrier(skc7))
| ex_sup_of_relstr_set(skc7,u) ),
inference(res,[status(thm),theory(equality)],[1,45]),
[iquote('0:Res:1.0,45.0')] ).
cnf(64,plain,
( ~ rel_str(skc7)
| ~ relstr_element_smaller(skc7,u,v)
| ~ related(skc7,skf13(v,u,skc7),v)
| ~ element(v,the_carrier(skc7))
| ex_inf_of_relstr_set(skc7,u) ),
inference(res,[status(thm),theory(equality)],[1,44]),
[iquote('0:Res:1.0,44.0')] ).
cnf(68,plain,
( ~ rel_str(skc7)
| ~ element(u,the_carrier(skc7))
| ~ relstr_element_smaller(skc7,v,u)
| relstr_element_smaller(skc7,v,skf13(u,v,skc7))
| ex_inf_of_relstr_set(skc7,v) ),
inference(res,[status(thm),theory(equality)],[1,39]),
[iquote('0:Res:1.0,39.0')] ).
cnf(71,plain,
( ~ one_sorted_str(skc7)
| ~ empty(the_carrier(skc7)) ),
inference(res,[status(thm),theory(equality)],[28,10]),
[iquote('0:Res:28.2,10.0')] ).
cnf(72,plain,
~ empty(the_carrier(skc7)),
inference(mrr,[status(thm)],[71,61]),
[iquote('0:MRR:71.0,61.0')] ).
cnf(73,plain,
relstr_element_smaller(skc7,the_carrier(skc7),skf7(skc7)),
inference(mrr,[status(thm)],[58,2]),
[iquote('0:MRR:58.0,2.0')] ).
cnf(76,plain,
( ~ element(u,the_carrier(skc7))
| ~ relstr_element_smaller(skc7,v,u)
| ex_inf_of_relstr_set(skc7,v)
| relstr_element_smaller(skc7,v,skf13(u,v,skc7)) ),
inference(mrr,[status(thm)],[68,3]),
[iquote('0:MRR:68.0,3.0')] ).
cnf(80,plain,
( ~ element(u,the_carrier(skc7))
| ~ relstr_element_smaller(skc7,v,u)
| ~ related(skc7,skf13(u,v,skc7),u)
| ex_inf_of_relstr_set(skc7,v) ),
inference(mrr,[status(thm)],[64,3]),
[iquote('0:MRR:64.0,3.0')] ).
cnf(81,plain,
( ~ element(u,the_carrier(skc7))
| ~ relstr_set_smaller(skc7,v,u)
| ~ related(skc7,u,skf11(u,v,skc7))
| ex_sup_of_relstr_set(skc7,v) ),
inference(mrr,[status(thm)],[63,3]),
[iquote('0:MRR:63.0,3.0')] ).
cnf(103,plain,
( empty(the_carrier(u))
| in(skf7(u),the_carrier(u)) ),
inference(res,[status(thm),theory(equality)],[16,29]),
[iquote('0:Res:16.0,29.0')] ).
cnf(107,plain,
( empty(the_carrier(u))
| in(skf11(v,w,u),the_carrier(u)) ),
inference(res,[status(thm),theory(equality)],[22,29]),
[iquote('0:Res:22.0,29.0')] ).
cnf(108,plain,
( empty(the_carrier(u))
| in(skf8(v,w,u),the_carrier(u)) ),
inference(res,[status(thm),theory(equality)],[21,29]),
[iquote('0:Res:21.0,29.0')] ).
cnf(157,plain,
( ~ in(u,v)
| ~ element(u,the_carrier(skc7))
| ~ relstr_element_smaller(skc7,v,skf7(skc7))
| related(skc7,skf7(skc7),u) ),
inference(res,[status(thm),theory(equality)],[16,48]),
[iquote('0:Res:16.0,48.1')] ).
cnf(168,plain,
( ~ rel_str(u)
| ~ in(v,w)
| ~ element(v,the_carrier(u))
| ~ relstr_element_smaller(u,w,skf13(x,y,u))
| related(u,skf13(x,y,u),v) ),
inference(res,[status(thm),theory(equality)],[23,43]),
[iquote('0:Res:23.0,43.2')] ).
cnf(172,plain,
( ~ in(u,the_carrier(skc7))
| ~ element(u,the_carrier(skc7))
| related(skc7,skf7(skc7),u) ),
inference(res,[status(thm),theory(equality)],[73,157]),
[iquote('0:Res:73.0,157.2')] ).
cnf(178,plain,
( ~ in(u,the_carrier(skc7))
| related(skc7,skf7(skc7),u) ),
inference(mrr,[status(thm)],[172,24]),
[iquote('0:MRR:172.1,24.1')] ).
cnf(180,plain,
( ~ in(skf8(skf7(skc7),u,skc7),the_carrier(skc7))
| ~ element(skf7(skc7),the_carrier(skc7))
| relstr_element_smaller(skc7,u,skf7(skc7)) ),
inference(res,[status(thm),theory(equality)],[178,53]),
[iquote('0:Res:178.1,53.1')] ).
cnf(183,plain,
( ~ in(skf8(skf7(skc7),u,skc7),the_carrier(skc7))
| relstr_element_smaller(skc7,u,skf7(skc7)) ),
inference(mrr,[status(thm)],[180,16]),
[iquote('0:MRR:180.1,16.0')] ).
cnf(185,plain,
( empty(the_carrier(skc7))
| relstr_element_smaller(skc7,u,skf7(skc7)) ),
inference(res,[status(thm),theory(equality)],[108,183]),
[iquote('0:Res:108.1,183.0')] ).
cnf(188,plain,
relstr_element_smaller(skc7,u,skf7(skc7)),
inference(mrr,[status(thm)],[185,72]),
[iquote('0:MRR:185.0,72.0')] ).
cnf(189,plain,
( ~ in(u,v)
| ~ element(u,the_carrier(skc7))
| related(skc7,skf7(skc7),u) ),
inference(mrr,[status(thm)],[157,188]),
[iquote('0:MRR:157.2,188.0')] ).
cnf(198,plain,
( ~ in(skf11(u,v,skc7),w)
| related(skc7,skf7(skc7),skf11(u,v,skc7)) ),
inference(res,[status(thm),theory(equality)],[22,189]),
[iquote('0:Res:22.0,189.1')] ).
cnf(218,plain,
( empty(the_carrier(skc7))
| related(skc7,skf7(skc7),skf11(u,v,skc7)) ),
inference(res,[status(thm),theory(equality)],[107,198]),
[iquote('0:Res:107.1,198.0')] ).
cnf(219,plain,
related(skc7,skf7(skc7),skf11(u,v,skc7)),
inference(mrr,[status(thm)],[218,72]),
[iquote('0:MRR:218.0,72.0')] ).
cnf(225,plain,
( ~ element(skf7(skc7),the_carrier(skc7))
| ~ relstr_set_smaller(skc7,u,skf7(skc7))
| ex_sup_of_relstr_set(skc7,u) ),
inference(res,[status(thm),theory(equality)],[219,81]),
[iquote('0:Res:219.0,81.2')] ).
cnf(227,plain,
( ~ relstr_set_smaller(skc7,u,skf7(skc7))
| ex_sup_of_relstr_set(skc7,u) ),
inference(mrr,[status(thm)],[225,16]),
[iquote('0:MRR:225.0,16.0')] ).
cnf(228,plain,
( ~ element(skf7(skc7),the_carrier(skc7))
| ex_sup_of_relstr_set(skc7,empty_set) ),
inference(res,[status(thm),theory(equality)],[59,227]),
[iquote('0:Res:59.1,227.0')] ).
cnf(230,plain,
ex_sup_of_relstr_set(skc7,empty_set),
inference(mrr,[status(thm)],[228,16]),
[iquote('0:MRR:228.0,16.0')] ).
cnf(231,plain,
~ ex_inf_of_relstr_set(skc7,the_carrier(skc7)),
inference(mrr,[status(thm)],[27,230]),
[iquote('0:MRR:27.0,230.0')] ).
cnf(423,plain,
( ~ rel_str(skc7)
| ~ element(u,the_carrier(skc7))
| ~ relstr_element_smaller(skc7,v,u)
| ~ in(w,v)
| ~ element(w,the_carrier(skc7))
| ex_inf_of_relstr_set(skc7,v)
| related(skc7,skf13(u,v,skc7),w) ),
inference(res,[status(thm),theory(equality)],[76,168]),
[iquote('0:Res:76.3,168.3')] ).
cnf(431,plain,
( ~ element(u,the_carrier(skc7))
| ~ relstr_element_smaller(skc7,v,u)
| ~ in(w,v)
| ~ element(w,the_carrier(skc7))
| ex_inf_of_relstr_set(skc7,v)
| related(skc7,skf13(u,v,skc7),w) ),
inference(ssi,[status(thm)],[423,2,1,3,61]),
[iquote('0:SSi:423.0,2.0,1.0,3.0,61.0')] ).
cnf(816,plain,
( ~ element(u,the_carrier(skc7))
| ~ relstr_element_smaller(skc7,v,u)
| ~ in(u,v)
| ~ element(u,the_carrier(skc7))
| ~ element(u,the_carrier(skc7))
| ~ relstr_element_smaller(skc7,v,u)
| ex_inf_of_relstr_set(skc7,v)
| ex_inf_of_relstr_set(skc7,v) ),
inference(res,[status(thm),theory(equality)],[431,80]),
[iquote('0:Res:431.5,80.2')] ).
cnf(820,plain,
( ~ in(u,v)
| ~ element(u,the_carrier(skc7))
| ~ relstr_element_smaller(skc7,v,u)
| ex_inf_of_relstr_set(skc7,v) ),
inference(obv,[status(thm),theory(equality)],[816]),
[iquote('0:Obv:816.6')] ).
cnf(827,plain,
( ~ in(skf7(skc7),u)
| ~ element(skf7(skc7),the_carrier(skc7))
| ex_inf_of_relstr_set(skc7,u) ),
inference(res,[status(thm),theory(equality)],[188,820]),
[iquote('0:Res:188.0,820.2')] ).
cnf(837,plain,
( ~ in(skf7(skc7),u)
| ex_inf_of_relstr_set(skc7,u) ),
inference(mrr,[status(thm)],[827,16]),
[iquote('0:MRR:827.1,16.0')] ).
cnf(846,plain,
( empty(the_carrier(skc7))
| ex_inf_of_relstr_set(skc7,the_carrier(skc7)) ),
inference(res,[status(thm),theory(equality)],[103,837]),
[iquote('0:Res:103.1,837.0')] ).
cnf(847,plain,
$false,
inference(mrr,[status(thm)],[846,72,231]),
[iquote('0:MRR:846.0,846.1,72.0,231.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU360+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 13:09:22 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.38/0.55
% 0.38/0.55 SPASS V 3.9
% 0.38/0.55 SPASS beiseite: Proof found.
% 0.38/0.55 % SZS status Theorem
% 0.38/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.55 SPASS derived 542 clauses, backtracked 0 clauses, performed 0 splits and kept 282 clauses.
% 0.38/0.55 SPASS allocated 104735 KBytes.
% 0.38/0.55 SPASS spent 0:00:00.17 on the problem.
% 0.38/0.55 0:00:00.04 for the input.
% 0.38/0.55 0:00:00.03 for the FLOTTER CNF translation.
% 0.38/0.55 0:00:00.02 for inferences.
% 0.38/0.55 0:00:00.00 for the backtracking.
% 0.38/0.55 0:00:00.05 for the reduction.
% 0.38/0.55
% 0.38/0.55
% 0.38/0.55 Here is a proof with depth 7, length 62 :
% 0.38/0.55 % SZS output start Refutation
% See solution above
% 0.38/0.55 Formulae used in the proof : t42_yellow_0 d4_yellow_0 existence_m1_subset_1 dt_l1_orders_2 d8_lattice3 t15_yellow_0 t16_yellow_0 t1_subset fc1_struct_0 t2_subset t6_yellow_0
% 0.38/0.55
%------------------------------------------------------------------------------