TSTP Solution File: SET843-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET843-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 05:29:10 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 29 ( 14 unt; 1 nHn; 29 RR)
% Number of literals : 49 ( 0 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 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,
( ~ c_in(u,v,tc_set(w))
| c_lessequals(u,c_Union(v,w),tc_set(w)) ),
file('SET843-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_lessequals(v,u,tc_set(w))
| equal(u,v) ),
file('SET843-2.p',unknown),
[] ).
cnf(3,axiom,
c_lessequals(u,u,tc_set(v)),
file('SET843-2.p',unknown),
[] ).
cnf(4,axiom,
c_lessequals(u,c_Zorn_Osucc(v,u,w),tc_set(tc_set(w))),
file('SET843-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| c_in(c_Zorn_Osucc(v,u,w),c_Zorn_OTFin(v,w),tc_set(tc_set(w))) ),
file('SET843-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_lessequals(u,c_Zorn_OTFin(v,w),tc_set(tc_set(tc_set(w))))
| c_in(c_Union(u,tc_set(w)),c_Zorn_OTFin(v,w),tc_set(tc_set(w))) ),
file('SET843-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(c_Zorn_Osucc(u,v,w),v)
| ~ c_in(x,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
| ~ c_in(v,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
| c_lessequals(x,v,tc_set(tc_set(w))) ),
file('SET843-2.p',unknown),
[] ).
cnf(8,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET843-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m)
| ~ equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m) ),
file('SET843-2.p',unknown),
[] ).
cnf(10,axiom,
( equal(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m)
| equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m) ),
file('SET843-2.p',unknown),
[] ).
cnf(12,plain,
c_lessequals(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.0')] ).
cnf(13,plain,
( ~ equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m)
| ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(u,v_m,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[8,7]),
[iquote('0:Res:8.0,7.0')] ).
cnf(14,plain,
c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[8,5]),
[iquote('0:Res:8.0,5.0')] ).
cnf(17,plain,
equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m),
inference(spt,[spt(split,[position(s1)])],[10]),
[iquote('1:Spt:10.1')] ).
cnf(18,plain,
( ~ equal(v_m,v_m)
| ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(u,v_m,tc_set(tc_set(t_a))) ),
inference(rew,[status(thm),theory(equality)],[17,13]),
[iquote('1:Rew:17.0,13.0')] ).
cnf(19,plain,
( ~ equal(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m)
| ~ equal(v_m,v_m) ),
inference(rew,[status(thm),theory(equality)],[17,9]),
[iquote('1:Rew:17.0,9.1')] ).
cnf(21,plain,
~ equal(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m),
inference(obv,[status(thm),theory(equality)],[19]),
[iquote('1:Obv:19.1')] ).
cnf(22,plain,
( ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(u,v_m,tc_set(tc_set(t_a))) ),
inference(obv,[status(thm),theory(equality)],[18]),
[iquote('1:Obv:18.0')] ).
cnf(29,plain,
( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| equal(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m) ),
inference(res,[status(thm),theory(equality)],[12,2]),
[iquote('0:Res:12.0,2.0')] ).
cnf(30,plain,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(mrr,[status(thm)],[29,21]),
[iquote('1:MRR:29.1,21.0')] ).
cnf(41,plain,
( ~ c_lessequals(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a))))
| c_lessequals(c_Union(u,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[6,22]),
[iquote('1:Res:6.1,22.0')] ).
cnf(46,plain,
~ c_lessequals(c_Zorn_OTFin(v_S,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
inference(res,[status(thm),theory(equality)],[41,30]),
[iquote('1:Res:41.1,30.0')] ).
cnf(48,plain,
$false,
inference(mrr,[status(thm)],[46,3]),
[iquote('1:MRR:46.0,3.0')] ).
cnf(49,plain,
~ equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m),
inference(spt,[spt(split,[position(sa)])],[48,17]),
[iquote('1:Spt:48.0,10.1,17.0')] ).
cnf(50,plain,
equal(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m),
inference(spt,[spt(split,[position(s2)])],[10]),
[iquote('1:Spt:48.0,10.0')] ).
cnf(54,plain,
( ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(u,v_m,tc_set(tc_set(t_a))) ),
inference(spr,[status(thm),theory(equality)],[50,1]),
[iquote('1:SpR:50.0,1.1')] ).
cnf(59,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[14,54]),
[iquote('1:Res:14.0,54.0')] ).
cnf(66,plain,
( ~ c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m) ),
inference(res,[status(thm),theory(equality)],[59,2]),
[iquote('1:Res:59.0,2.0')] ).
cnf(69,plain,
$false,
inference(mrr,[status(thm)],[66,4,49]),
[iquote('1:MRR:66.0,66.1,4.0,49.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET843-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 04:44:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 50 clauses, backtracked 6 clauses, performed 1 splits and kept 44 clauses.
% 0.19/0.43 SPASS allocated 63167 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.43 0:00:00.04 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.00 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 4, length 29 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : cls_Set_OUnion__upper_0 cls_Set_Osubset__antisym_0 cls_Set_Osubset__refl_0 cls_Zorn_OAbrial__axiom1_0 cls_Zorn_OTFin_OsuccI_0 cls_Zorn_OTFin__UnionI_0 cls_Zorn_Oeq__succ__upper_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2
% 0.19/0.43
%------------------------------------------------------------------------------