TSTP Solution File: SWV260-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV260-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 21:41:52 EDT 2022
% Result : Unsatisfiable 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 25 ( 8 unt; 6 nHn; 25 RR)
% Number of literals : 46 ( 0 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(u,v,tc_Message_Omsg)
| c_in(u,c_Message_Oparts(v),tc_Message_Omsg) ),
file('SWV260-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_union(x,v,w),w) ),
file('SWV260-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_union(v,x,w),w) ),
file('SWV260-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,c_insert(v,w,x),x)
| equal(u,v)
| c_in(u,w,x) ),
file('SWV260-2.p',unknown),
[] ).
cnf(5,axiom,
( c_lessequals(u,v,tc_set(w))
| c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
file('SWV260-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
| c_lessequals(u,v,tc_set(w)) ),
file('SWV260-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_in(u,c_Message_Oparts(v),tc_Message_Omsg)
| ~ c_lessequals(v,c_Message_Oparts(w),tc_set(tc_Message_Omsg))
| c_in(u,c_Message_Oparts(w),tc_Message_Omsg) ),
file('SWV260-2.p',unknown),
[] ).
cnf(8,axiom,
c_in(v_Y,c_Message_Oparts(c_insert(v_X,v_G,tc_Message_Omsg)),tc_Message_Omsg),
file('SWV260-2.p',unknown),
[] ).
cnf(9,axiom,
c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg),
file('SWV260-2.p',unknown),
[] ).
cnf(10,axiom,
~ c_in(v_Y,c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),
file('SWV260-2.p',unknown),
[] ).
cnf(11,plain,
( ~ c_lessequals(v_H,c_Message_Oparts(u),tc_set(tc_Message_Omsg))
| c_in(v_X,c_Message_Oparts(u),tc_Message_Omsg) ),
inference(res,[status(thm),theory(equality)],[9,7]),
[iquote('0:Res:9.0,7.0')] ).
cnf(20,plain,
( ~ c_lessequals(u,c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(v_Y,c_Message_Oparts(u),tc_Message_Omsg) ),
inference(res,[status(thm),theory(equality)],[7,10]),
[iquote('0:Res:7.2,10.0')] ).
cnf(22,plain,
~ c_lessequals(c_insert(v_X,v_G,tc_Message_Omsg),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[8,20]),
[iquote('0:Res:8.0,20.0')] ).
cnf(27,plain,
( ~ c_in(c_Main_OsubsetI__1(u,c_Message_Oparts(v),tc_Message_Omsg),v,tc_Message_Omsg)
| c_lessequals(u,c_Message_Oparts(v),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[1,6]),
[iquote('0:Res:1.1,6.0')] ).
cnf(32,plain,
( c_lessequals(c_insert(u,v,w),x,tc_set(w))
| equal(c_Main_OsubsetI__1(c_insert(u,v,w),x,w),u)
| c_in(c_Main_OsubsetI__1(c_insert(u,v,w),x,w),v,w) ),
inference(res,[status(thm),theory(equality)],[5,4]),
[iquote('0:Res:5.1,4.0')] ).
cnf(35,plain,
( ~ c_in(c_Main_OsubsetI__1(u,c_Message_Oparts(c_union(v,w,tc_Message_Omsg)),tc_Message_Omsg),v,tc_Message_Omsg)
| c_lessequals(u,c_Message_Oparts(c_union(v,w,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[3,27]),
[iquote('0:Res:3.1,27.0')] ).
cnf(36,plain,
( ~ c_in(c_Main_OsubsetI__1(u,c_Message_Oparts(c_union(v,w,tc_Message_Omsg)),tc_Message_Omsg),w,tc_Message_Omsg)
| c_lessequals(u,c_Message_Oparts(c_union(v,w,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[2,27]),
[iquote('0:Res:2.1,27.0')] ).
cnf(130,plain,
( c_lessequals(u,c_Message_Oparts(c_union(v,u,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_lessequals(u,c_Message_Oparts(c_union(v,u,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[5,36]),
[iquote('0:Res:5.1,36.0')] ).
cnf(134,plain,
c_lessequals(u,c_Message_Oparts(c_union(v,u,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(obv,[status(thm),theory(equality)],[130]),
[iquote('0:Obv:130.0')] ).
cnf(137,plain,
c_in(v_X,c_Message_Oparts(c_union(u,v_H,tc_Message_Omsg)),tc_Message_Omsg),
inference(res,[status(thm),theory(equality)],[134,11]),
[iquote('0:Res:134.0,11.0')] ).
cnf(146,plain,
( c_lessequals(c_insert(u,v,tc_Message_Omsg),c_Message_Oparts(c_union(v,w,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| equal(c_Main_OsubsetI__1(c_insert(u,v,tc_Message_Omsg),c_Message_Oparts(c_union(v,w,tc_Message_Omsg)),tc_Message_Omsg),u)
| c_lessequals(c_insert(u,v,tc_Message_Omsg),c_Message_Oparts(c_union(v,w,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[32,35]),
[iquote('0:Res:32.2,35.0')] ).
cnf(151,plain,
( equal(c_Main_OsubsetI__1(c_insert(u,v,tc_Message_Omsg),c_Message_Oparts(c_union(v,w,tc_Message_Omsg)),tc_Message_Omsg),u)
| c_lessequals(c_insert(u,v,tc_Message_Omsg),c_Message_Oparts(c_union(v,w,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(obv,[status(thm),theory(equality)],[146]),
[iquote('0:Obv:146.0')] ).
cnf(700,plain,
equal(c_Main_OsubsetI__1(c_insert(v_X,v_G,tc_Message_Omsg),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg),v_X),
inference(res,[status(thm),theory(equality)],[151,22]),
[iquote('0:Res:151.1,22.0')] ).
cnf(707,plain,
( ~ c_in(v_X,c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_G,tc_Message_Omsg),c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(spl,[status(thm),theory(equality)],[700,6]),
[iquote('0:SpL:700.0,6.0')] ).
cnf(713,plain,
$false,
inference(mrr,[status(thm)],[707,137,22]),
[iquote('0:MRR:707.0,707.1,137.0,22.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV260-2 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n018.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 : Wed Jun 15 10:22:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.55
% 0.20/0.55 SPASS V 3.9
% 0.20/0.55 SPASS beiseite: Proof found.
% 0.20/0.55 % SZS status Theorem
% 0.20/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.55 SPASS derived 569 clauses, backtracked 0 clauses, performed 0 splits and kept 446 clauses.
% 0.20/0.55 SPASS allocated 64149 KBytes.
% 0.20/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.20/0.55 0:00:00.03 for the input.
% 0.20/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.55 0:00:00.02 for inferences.
% 0.20/0.55 0:00:00.00 for the backtracking.
% 0.20/0.55 0:00:00.12 for the reduction.
% 0.20/0.55
% 0.20/0.55
% 0.20/0.55 Here is a proof with depth 5, length 25 :
% 0.20/0.55 % SZS output start Refutation
% See solution above
% 0.20/0.55 Formulae used in the proof : cls_Message_Oparts_OInj_0 cls_Set_OUnCI_0 cls_Set_OUnCI_1 cls_Set_OinsertE_0 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1 cls_Message_Oparts__trans_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2
% 0.20/0.55
%------------------------------------------------------------------------------