TSTP Solution File: SWV249-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV249-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 : Wed Jul 20 21:41:48 EDT 2022
% Result : Unsatisfiable 1.82s 2.07s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of clauses : 47 ( 26 unt; 0 nHn; 47 RR)
% Number of literals : 74 ( 0 equ; 31 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(c_Message_Oanalz(c_union(c_Message_Oanalz(u),v,tc_Message_Omsg)),c_Message_Oanalz(c_union(u,v,tc_Message_Omsg))),
file('SWV249-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_lessequals(u,v,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(u),c_Message_Oanalz(v),tc_set(tc_Message_Omsg)) ),
file('SWV249-2.p',unknown),
[] ).
cnf(3,axiom,
equal(c_union(c_Message_Oanalz(c_union(u,v,tc_Message_Omsg)),c_Message_Osynth(u),tc_Message_Omsg),c_Message_Oanalz(c_union(c_Message_Osynth(u),v,tc_Message_Omsg))),
file('SWV249-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Orderings_Oorder(u)
| c_lessequals(v,v,u) ),
file('SWV249-2.p',unknown),
[] ).
cnf(5,axiom,
equal(c_union(c_minus(u,v,tc_set(w)),v,w),c_union(u,v,w)),
file('SWV249-2.p',unknown),
[] ).
cnf(6,axiom,
equal(c_union(u,c_minus(v,u,tc_set(w)),w),c_union(u,v,w)),
file('SWV249-2.p',unknown),
[] ).
cnf(7,axiom,
equal(c_union(c_insert(u,v,w),x,w),c_insert(u,c_union(v,x,w),w)),
file('SWV249-2.p',unknown),
[] ).
cnf(8,axiom,
equal(c_union(u,c_insert(v,w,x),x),c_insert(v,c_union(u,w,x),x)),
file('SWV249-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ c_lessequals(c_union(u,v,w),x,tc_set(w))
| c_lessequals(u,x,tc_set(w)) ),
file('SWV249-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ c_lessequals(c_union(u,v,w),x,tc_set(w))
| c_lessequals(v,x,tc_set(w)) ),
file('SWV249-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_lessequals(x,v,tc_set(w))
| c_lessequals(c_union(u,x,w),v,tc_set(w)) ),
file('SWV249-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ c_lessequals(c_insert(u,v,w),x,tc_set(w))
| c_lessequals(v,x,tc_set(w)) ),
file('SWV249-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ c_in(u,v,w)
| ~ c_lessequals(x,v,tc_set(w))
| c_lessequals(c_insert(u,x,w),v,tc_set(w)) ),
file('SWV249-2.p',unknown),
[] ).
cnf(14,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_lessequals(v,u,tc_set(w))
| equal(u,v) ),
file('SWV249-2.p',unknown),
[] ).
cnf(15,axiom,
class_Orderings_Oorder(tc_set(u)),
file('SWV249-2.p',unknown),
[] ).
cnf(16,axiom,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
file('SWV249-2.p',unknown),
[] ).
cnf(17,axiom,
~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
file('SWV249-2.p',unknown),
[] ).
cnf(18,plain,
( ~ c_lessequals(u,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg))
| c_lessequals(c_insert(v_X,u,tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[16,13]),
[iquote('0:Res:16.0,13.0')] ).
cnf(31,plain,
( ~ class_Orderings_Oorder(tc_set(u))
| c_lessequals(v,c_insert(w,v,u),tc_set(u)) ),
inference(res,[status(thm),theory(equality)],[4,12]),
[iquote('0:Res:4.1,12.0')] ).
cnf(32,plain,
c_lessequals(u,c_insert(v,u,w),tc_set(w)),
inference(ssi,[status(thm)],[31,15]),
[iquote('0:SSi:31.0,15.0')] ).
cnf(36,plain,
( ~ class_Orderings_Oorder(tc_set(u))
| c_lessequals(v,c_union(w,v,u),tc_set(u)) ),
inference(res,[status(thm),theory(equality)],[4,10]),
[iquote('0:Res:4.1,10.0')] ).
cnf(38,plain,
c_lessequals(u,c_union(v,u,w),tc_set(w)),
inference(ssi,[status(thm)],[36,15]),
[iquote('0:SSi:36.0,15.0')] ).
cnf(59,plain,
( ~ class_Orderings_Oorder(tc_set(u))
| c_lessequals(v,c_union(v,w,u),tc_set(u)) ),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.1,9.0')] ).
cnf(65,plain,
c_lessequals(u,c_union(u,v,w),tc_set(w)),
inference(ssi,[status(thm)],[59,15]),
[iquote('0:SSi:59.0,15.0')] ).
cnf(66,plain,
c_lessequals(c_minus(u,v,tc_set(w)),c_union(u,v,w),tc_set(w)),
inference(spr,[status(thm),theory(equality)],[5,65]),
[iquote('0:SpR:5.0,65.0')] ).
cnf(94,plain,
( ~ c_lessequals(c_insert(u,v,w),v,tc_set(w))
| equal(c_insert(u,v,w),v) ),
inference(res,[status(thm),theory(equality)],[32,14]),
[iquote('0:Res:32.0,14.0')] ).
cnf(121,plain,
c_lessequals(c_insert(u,v,w),c_insert(u,c_union(v,x,w),w),tc_set(w)),
inference(spr,[status(thm),theory(equality)],[7,65]),
[iquote('0:SpR:7.0,65.0')] ).
cnf(294,plain,
equal(c_union(c_Message_Oanalz(c_union(u,v,tc_Message_Omsg)),c_Message_Osynth(c_Message_Oanalz(u)),tc_Message_Omsg),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(u)),v,tc_Message_Omsg))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(422,plain,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_lessequals(c_minus(x,u,tc_set(w)),v,tc_set(w))
| c_lessequals(c_union(u,x,w),v,tc_set(w)) ),
inference(spr,[status(thm),theory(equality)],[6,11]),
[iquote('0:SpR:6.0,11.2')] ).
cnf(568,plain,
( ~ c_in(u,v,w)
| ~ c_lessequals(v,v,tc_set(w))
| equal(c_insert(u,v,w),v) ),
inference(res,[status(thm),theory(equality)],[13,94]),
[iquote('0:Res:13.2,94.0')] ).
cnf(914,plain,
( ~ c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg))
| equal(c_insert(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G))) ),
inference(res,[status(thm),theory(equality)],[18,94]),
[iquote('0:Res:18.1,94.0')] ).
cnf(2422,plain,
( ~ class_Orderings_Oorder(tc_set(u))
| ~ c_in(v,w,u)
| equal(c_insert(v,w,u),w) ),
inference(res,[status(thm),theory(equality)],[4,568]),
[iquote('0:Res:4.1,568.1')] ).
cnf(2430,plain,
( ~ c_in(u,v,w)
| equal(c_insert(u,v,w),v) ),
inference(ssi,[status(thm)],[2422,15]),
[iquote('0:SSi:2422.0,15.0')] ).
cnf(2438,plain,
( ~ c_in(u,v,w)
| c_lessequals(v,v,tc_set(w)) ),
inference(spr,[status(thm),theory(equality)],[2430,32]),
[iquote('0:SpR:2430.1,32.0')] ).
cnf(2502,plain,
c_lessequals(c_Message_Osynth(c_Message_Oanalz(v_G)),c_Message_Osynth(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[16,2438]),
[iquote('0:Res:16.0,2438.0')] ).
cnf(2503,plain,
equal(c_insert(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),c_Message_Osynth(c_Message_Oanalz(v_G))),
inference(mrr,[status(thm)],[914,2502]),
[iquote('0:MRR:914.0,2502.0')] ).
cnf(2607,plain,
equal(c_insert(v_X,c_union(u,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),tc_Message_Omsg),c_union(u,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)),
inference(spr,[status(thm),theory(equality)],[2503,8]),
[iquote('0:SpR:2503.0,8.0')] ).
cnf(2756,plain,
c_lessequals(c_insert(v_X,u,tc_Message_Omsg),c_union(u,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(spr,[status(thm),theory(equality)],[2607,121]),
[iquote('0:SpR:2607.0,121.0')] ).
cnf(3218,plain,
( ~ c_lessequals(u,c_union(v,u,w),tc_set(w))
| c_lessequals(c_union(u,v,w),c_union(v,u,w),tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[66,422]),
[iquote('0:Res:66.0,422.1')] ).
cnf(3251,plain,
c_lessequals(c_union(u,v,w),c_union(v,u,w),tc_set(w)),
inference(mrr,[status(thm)],[3218,38]),
[iquote('0:MRR:3218.0,38.0')] ).
cnf(3282,plain,
( ~ c_lessequals(c_union(u,v,w),c_union(v,u,w),tc_set(w))
| equal(c_union(v,u,w),c_union(u,v,w)) ),
inference(res,[status(thm),theory(equality)],[3251,14]),
[iquote('0:Res:3251.0,14.0')] ).
cnf(3291,plain,
equal(c_union(u,v,w),c_union(v,u,w)),
inference(mrr,[status(thm)],[3282,3251]),
[iquote('0:MRR:3282.0,3251.0')] ).
cnf(3299,plain,
equal(c_union(c_Message_Osynth(c_Message_Oanalz(u)),c_Message_Oanalz(c_union(u,v,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(u)),v,tc_Message_Omsg))),
inference(rew,[status(thm),theory(equality)],[3291,294]),
[iquote('0:Rew:3291.0,294.0')] ).
cnf(3555,plain,
~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(rew,[status(thm),theory(equality)],[3299,17]),
[iquote('0:Rew:3299.0,17.0')] ).
cnf(3567,plain,
~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(rew,[status(thm),theory(equality)],[3291,3555]),
[iquote('0:Rew:3291.0,3555.0')] ).
cnf(4317,plain,
~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_H,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[2,3567]),
[iquote('0:Res:2.1,3567.0')] ).
cnf(4319,plain,
$false,
inference(mrr,[status(thm)],[4317,2756]),
[iquote('0:MRR:4317.0,2756.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV249-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n014.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 : Tue Jun 14 22:28:36 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.82/2.07
% 1.82/2.07 SPASS V 3.9
% 1.82/2.07 SPASS beiseite: Proof found.
% 1.82/2.07 % SZS status Theorem
% 1.82/2.07 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.82/2.07 SPASS derived 3562 clauses, backtracked 0 clauses, performed 0 splits and kept 1752 clauses.
% 1.82/2.07 SPASS allocated 81998 KBytes.
% 1.82/2.07 SPASS spent 0:00:01.67 on the problem.
% 1.82/2.07 0:00:00.04 for the input.
% 1.82/2.07 0:00:00.00 for the FLOTTER CNF translation.
% 1.82/2.07 0:00:00.05 for inferences.
% 1.82/2.07 0:00:00.00 for the backtracking.
% 1.82/2.07 0:00:01.56 for the reduction.
% 1.82/2.07
% 1.82/2.07
% 1.82/2.07 Here is a proof with depth 6, length 47 :
% 1.82/2.07 % SZS output start Refutation
% See solution above
% 1.82/2.07 Formulae used in the proof : cls_Message_Oanalz__analz__Un_0 cls_Message_Oanalz__mono_0 cls_Message_Oanalz__synth__Un_0 cls_Orderings_Oorder__class_Oaxioms__1_0 cls_Set_OUn__Diff__cancel2_0 cls_Set_OUn__Diff__cancel_0 cls_Set_OUn__insert__left_0 cls_Set_OUn__insert__right_0 cls_Set_OUn__subset__iff_0 cls_Set_OUn__subset__iff_1 cls_Set_OUn__subset__iff_2 cls_Set_Oinsert__subset_1 cls_Set_Oinsert__subset_2 cls_Set_Osubset__antisym_0 clsarity_set_2 cls_conjecture_0 cls_conjecture_1
% 1.82/2.07
%------------------------------------------------------------------------------