TSTP Solution File: SWV261-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV261-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 21:41:53 EDT 2022
% Result : Unsatisfiable 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 21 ( 7 unt; 5 nHn; 21 RR)
% Number of literals : 39 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
c_lessequals(c_Message_Oparts(c_union(u,v,tc_Message_Omsg)),c_union(c_Message_Oparts(u),c_Message_Oparts(v),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
file('SWV261-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_lessequals(u,v,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(u),c_Message_Oparts(v),tc_set(tc_Message_Omsg)) ),
file('SWV261-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_union(x,v,w),w) ),
file('SWV261-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_union(v,x,w),w) ),
file('SWV261-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(u,c_insert(v,w,x),x)
| equal(u,v)
| c_in(u,w,x) ),
file('SWV261-2.p',unknown),
[] ).
cnf(6,axiom,
( c_lessequals(u,v,tc_set(w))
| c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
file('SWV261-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
| c_lessequals(u,v,tc_set(w)) ),
file('SWV261-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_lessequals(v,x,tc_set(w))
| c_lessequals(u,x,tc_set(w)) ),
file('SWV261-2.p',unknown),
[] ).
cnf(9,axiom,
c_in(v_X,v_G,tc_Message_Omsg),
file('SWV261-2.p',unknown),
[] ).
cnf(10,axiom,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
file('SWV261-2.p',unknown),
[] ).
cnf(15,plain,
( ~ c_lessequals(u,c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),u,tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[8,10]),
[iquote('0:Res:8.2,10.0')] ).
cnf(17,plain,
( ~ c_in(c_Main_OsubsetI__1(u,c_union(v,w,x),x),v,x)
| c_lessequals(u,c_union(v,w,x),tc_set(x)) ),
inference(res,[status(thm),theory(equality)],[4,7]),
[iquote('0:Res:4.1,7.0')] ).
cnf(18,plain,
( ~ c_in(c_Main_OsubsetI__1(u,c_union(v,w,x),x),w,x)
| c_lessequals(u,c_union(v,w,x),tc_set(x)) ),
inference(res,[status(thm),theory(equality)],[3,7]),
[iquote('0:Res:3.1,7.0')] ).
cnf(20,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)],[6,5]),
[iquote('0:Res:6.1,5.0')] ).
cnf(91,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,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)],[1,15]),
[iquote('0:Res:1.0,15.0')] ).
cnf(97,plain,
( c_lessequals(c_insert(u,v,w),c_union(x,v,w),tc_set(w))
| equal(c_Main_OsubsetI__1(c_insert(u,v,w),c_union(x,v,w),w),u)
| c_lessequals(c_insert(u,v,w),c_union(x,v,w),tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[20,18]),
[iquote('0:Res:20.2,18.0')] ).
cnf(99,plain,
( equal(c_Main_OsubsetI__1(c_insert(u,v,w),c_union(x,v,w),w),u)
| c_lessequals(c_insert(u,v,w),c_union(x,v,w),tc_set(w)) ),
inference(obv,[status(thm),theory(equality)],[97]),
[iquote('0:Obv:97.0')] ).
cnf(101,plain,
~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(res,[status(thm),theory(equality)],[2,91]),
[iquote('0:Res:2.1,91.0')] ).
cnf(196,plain,
equal(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_X),
inference(res,[status(thm),theory(equality)],[99,101]),
[iquote('0:Res:99.1,101.0')] ).
cnf(202,plain,
( ~ c_in(v_X,v_G,tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(spl,[status(thm),theory(equality)],[196,17]),
[iquote('0:SpL:196.0,17.0')] ).
cnf(204,plain,
$false,
inference(mrr,[status(thm)],[202,9,101]),
[iquote('0:MRR:202.0,202.1,9.0,101.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV261-2 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Wed Jun 15 03:12:40 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.48
% 0.21/0.48 SPASS V 3.9
% 0.21/0.48 SPASS beiseite: Proof found.
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48 SPASS derived 183 clauses, backtracked 0 clauses, performed 0 splits and kept 171 clauses.
% 0.21/0.48 SPASS allocated 63411 KBytes.
% 0.21/0.48 SPASS spent 0:00:00.10 on the problem.
% 0.21/0.48 0:00:00.04 for the input.
% 0.21/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.48 0:00:00.01 for inferences.
% 0.21/0.48 0:00:00.00 for the backtracking.
% 0.21/0.48 0:00:00.04 for the reduction.
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Here is a proof with depth 5, length 21 :
% 0.21/0.48 % SZS output start Refutation
% See solution above
% 0.21/0.48 Formulae used in the proof : cls_Message_Oparts__Un__subset2_0 cls_Message_Oparts__mono_0 cls_Set_OUnCI_0 cls_Set_OUnCI_1 cls_Set_OinsertE_0 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1 cls_Set_Osubset__trans_0 cls_conjecture_0 cls_conjecture_1
% 0.21/0.48
%------------------------------------------------------------------------------