TSTP Solution File: SWV276-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV276-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 21:41:59 EDT 2022
% Result : Unsatisfiable 3.84s 4.08s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of clauses : 49 ( 19 unt; 12 nHn; 49 RR)
% Number of literals : 93 ( 0 equ; 38 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(u,c_Message_OkeysFor(c_Message_Osynth(v)),tc_nat)
| c_in(u,c_Message_OkeysFor(v),tc_nat)
| c_in(c_Message_Omsg_OKey(v_sko__uhi(v,u)),v,tc_Message_Omsg) ),
file('SWV276-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,c_Message_OkeysFor(c_Message_Osynth(v)),tc_nat)
| equal(c_Message_OinvKey(v_sko__uhi(v,u)),u)
| c_in(u,c_Message_OkeysFor(v),tc_nat) ),
file('SWV276-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,c_Message_Oanalz(v),tc_Message_Omsg)
| c_in(u,c_Message_Oparts(v),tc_Message_Omsg) ),
file('SWV276-2.p',unknown),
[] ).
cnf(4,axiom,
c_lessequals(c_Message_Oanalz(u),c_Message_Oparts(u),tc_set(tc_Message_Omsg)),
file('SWV276-2.p',unknown),
[] ).
cnf(5,axiom,
equal(c_Message_OinvKey(c_Message_OinvKey(u)),u),
file('SWV276-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_lessequals(u,v,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_OkeysFor(u),c_Message_OkeysFor(v),tc_set(tc_nat)) ),
file('SWV276-2.p',unknown),
[] ).
cnf(7,axiom,
equal(c_union(c_Message_OkeysFor(u),c_Message_OkeysFor(v),tc_nat),c_Message_OkeysFor(c_union(u,v,tc_Message_Omsg))),
file('SWV276-2.p',unknown),
[] ).
cnf(8,axiom,
equal(c_Message_Oparts(c_Message_Oanalz(u)),c_Message_Oparts(u)),
file('SWV276-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ c_in(u,v,tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_insert(u,w,tc_Message_Omsg)),c_union(c_Message_Oparts(v),c_Message_Oparts(w),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
file('SWV276-2.p',unknown),
[] ).
cnf(10,axiom,
equal(c_union(c_Message_Oparts(u),c_Message_Osynth(u),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(u))),
file('SWV276-2.p',unknown),
[] ).
cnf(11,axiom,
equal(c_union(c_Message_Oparts(u),c_Message_Oparts(v),tc_Message_Omsg),c_Message_Oparts(c_union(u,v,tc_Message_Omsg))),
file('SWV276-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ c_in(u,v,w)
| ~ c_lessequals(v,x,tc_set(w))
| c_in(u,x,w) ),
file('SWV276-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ c_in(u,c_union(v,w,x),x)
| c_in(u,v,x)
| c_in(u,w,x) ),
file('SWV276-2.p',unknown),
[] ).
cnf(14,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_union(v,x,w),w) ),
file('SWV276-2.p',unknown),
[] ).
cnf(15,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_union(x,v,w),w) ),
file('SWV276-2.p',unknown),
[] ).
cnf(16,axiom,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(v_X,v_G,tc_Message_Omsg))),tc_nat),
file('SWV276-2.p',unknown),
[] ).
cnf(17,axiom,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_H)),tc_Message_Omsg),
file('SWV276-2.p',unknown),
[] ).
cnf(18,axiom,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg))),tc_nat),
file('SWV276-2.p',unknown),
[] ).
cnf(19,axiom,
~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Oparts(v_H),tc_Message_Omsg),
file('SWV276-2.p',unknown),
[] ).
cnf(20,plain,
( ~ c_in(u,v,tc_Message_Omsg)
| c_lessequals(c_Message_Oparts(c_insert(u,w,tc_Message_Omsg)),c_Message_Oparts(c_union(v,w,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(rew,[status(thm),theory(equality)],[11,9]),
[iquote('0:Rew:11.0,9.1')] ).
cnf(25,plain,
~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Oanalz(v_H),tc_Message_Omsg),
inference(res,[status(thm),theory(equality)],[3,19]),
[iquote('0:Res:3.1,19.0')] ).
cnf(29,plain,
( ~ c_lessequals(c_Message_OkeysFor(c_Message_Oparts(c_insert(v_X,v_G,tc_Message_Omsg))),u,tc_set(tc_nat))
| c_in(v_K,u,tc_nat) ),
inference(res,[status(thm),theory(equality)],[16,12]),
[iquote('0:Res:16.0,12.0')] ).
cnf(51,plain,
equal(c_union(c_Message_Oparts(u),c_Message_Osynth(c_Message_Oanalz(u)),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(u)))),
inference(spr,[status(thm),theory(equality)],[8,10]),
[iquote('0:SpR:8.0,10.0')] ).
cnf(98,plain,
( ~ c_in(u,c_Message_OkeysFor(v),tc_nat)
| c_in(u,c_Message_OkeysFor(c_union(w,v,tc_Message_Omsg)),tc_nat) ),
inference(spr,[status(thm),theory(equality)],[7,15]),
[iquote('0:SpR:7.0,15.1')] ).
cnf(102,plain,
( ~ c_in(u,c_Message_OkeysFor(v),tc_nat)
| c_in(u,c_Message_OkeysFor(c_union(v,w,tc_Message_Omsg)),tc_nat) ),
inference(spr,[status(thm),theory(equality)],[7,14]),
[iquote('0:SpR:7.0,14.1')] ).
cnf(120,plain,
( ~ c_lessequals(u,v,tc_set(tc_Message_Omsg))
| ~ c_in(w,c_Message_OkeysFor(u),tc_nat)
| c_in(w,c_Message_OkeysFor(v),tc_nat) ),
inference(res,[status(thm),theory(equality)],[6,12]),
[iquote('0:Res:6.1,12.1')] ).
cnf(124,plain,
( ~ c_in(u,c_Message_OkeysFor(c_union(v,w,tc_Message_Omsg)),tc_nat)
| c_in(u,c_Message_OkeysFor(v),tc_nat)
| c_in(u,c_Message_OkeysFor(w),tc_nat) ),
inference(spl,[status(thm),theory(equality)],[7,13]),
[iquote('0:SpL:7.0,13.0')] ).
cnf(171,plain,
( ~ c_in(u,c_Message_OkeysFor(c_Message_Oparts(v)),tc_nat)
| c_in(u,c_Message_OkeysFor(c_Message_Oparts(c_union(w,v,tc_Message_Omsg))),tc_nat) ),
inference(spr,[status(thm),theory(equality)],[11,98]),
[iquote('0:SpR:11.0,98.1')] ).
cnf(187,plain,
( ~ c_in(u,c_Message_OkeysFor(c_Message_Oparts(v)),tc_nat)
| c_in(u,c_Message_OkeysFor(c_Message_Oparts(c_union(v,w,tc_Message_Omsg))),tc_nat) ),
inference(spr,[status(thm),theory(equality)],[11,102]),
[iquote('0:SpR:11.0,102.1')] ).
cnf(188,plain,
( ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_G,tc_Message_Omsg)),u,tc_set(tc_Message_Omsg))
| c_in(v_K,c_Message_OkeysFor(u),tc_nat) ),
inference(res,[status(thm),theory(equality)],[6,29]),
[iquote('0:Res:6.1,29.0')] ).
cnf(194,plain,
( ~ c_in(v_X,u,tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(u,v_G,tc_Message_Omsg))),tc_nat) ),
inference(res,[status(thm),theory(equality)],[20,188]),
[iquote('0:Res:20.1,188.0')] ).
cnf(252,plain,
( ~ c_in(u,c_Message_OkeysFor(c_Message_Oanalz(v)),tc_nat)
| c_in(u,c_Message_OkeysFor(c_Message_Oparts(v)),tc_nat) ),
inference(res,[status(thm),theory(equality)],[4,120]),
[iquote('0:Res:4.0,120.0')] ).
cnf(326,plain,
( ~ c_in(u,c_Message_OkeysFor(c_Message_Oparts(c_Message_Osynth(c_Message_Oanalz(v)))),tc_nat)
| c_in(u,c_Message_OkeysFor(c_Message_Oparts(v)),tc_nat)
| c_in(u,c_Message_OkeysFor(c_Message_Osynth(c_Message_Oanalz(v))),tc_nat) ),
inference(spl,[status(thm),theory(equality)],[51,124]),
[iquote('0:SpL:51.0,124.0')] ).
cnf(328,plain,
( ~ c_in(u,c_Message_OkeysFor(c_Message_Oparts(c_union(v,w,tc_Message_Omsg))),tc_nat)
| c_in(u,c_Message_OkeysFor(c_Message_Oparts(v)),tc_nat)
| c_in(u,c_Message_OkeysFor(c_Message_Oparts(w)),tc_nat) ),
inference(spl,[status(thm),theory(equality)],[11,124]),
[iquote('0:SpL:11.0,124.0')] ).
cnf(445,plain,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_nat),
inference(res,[status(thm),theory(equality)],[171,18]),
[iquote('0:Res:171.1,18.0')] ).
cnf(447,plain,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat),
inference(res,[status(thm),theory(equality)],[252,445]),
[iquote('0:Res:252.1,445.0')] ).
cnf(484,plain,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_G)),tc_nat),
inference(res,[status(thm),theory(equality)],[187,18]),
[iquote('0:Res:187.1,18.0')] ).
cnf(1703,plain,
( ~ c_in(v_X,u,tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(u)),tc_nat)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_G)),tc_nat) ),
inference(res,[status(thm),theory(equality)],[194,328]),
[iquote('0:Res:194.1,328.0')] ).
cnf(1707,plain,
( ~ c_in(v_X,u,tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(u)),tc_nat) ),
inference(mrr,[status(thm)],[1703,484]),
[iquote('0:MRR:1703.2,484.0')] ).
cnf(1732,plain,
( ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(u)),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(u)),tc_nat)
| c_in(v_K,c_Message_OkeysFor(c_Message_Osynth(c_Message_Oanalz(u))),tc_nat) ),
inference(res,[status(thm),theory(equality)],[1707,326]),
[iquote('0:Res:1707.1,326.0')] ).
cnf(5810,plain,
( ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(u)),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(u)),tc_nat)
| equal(c_Message_OinvKey(v_sko__uhi(c_Message_Oanalz(u),v_K)),v_K)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(u)),tc_nat) ),
inference(res,[status(thm),theory(equality)],[1732,2]),
[iquote('0:Res:1732.2,2.0')] ).
cnf(5811,plain,
( ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(u)),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(u)),tc_nat)
| equal(c_Message_OinvKey(v_sko__uhi(c_Message_Oanalz(u),v_K)),v_K) ),
inference(mrr,[status(thm)],[5810,252]),
[iquote('0:MRR:5810.3,252.0')] ).
cnf(6947,plain,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_nat)
| equal(c_Message_OinvKey(v_sko__uhi(c_Message_Oanalz(v_H),v_K)),v_K) ),
inference(res,[status(thm),theory(equality)],[17,5811]),
[iquote('0:Res:17.0,5811.0')] ).
cnf(6948,plain,
equal(c_Message_OinvKey(v_sko__uhi(c_Message_Oanalz(v_H),v_K)),v_K),
inference(mrr,[status(thm)],[6947,445]),
[iquote('0:MRR:6947.0,445.0')] ).
cnf(6949,plain,
equal(v_sko__uhi(c_Message_Oanalz(v_H),v_K),c_Message_OinvKey(v_K)),
inference(spr,[status(thm),theory(equality)],[6948,5]),
[iquote('0:SpR:6948.0,5.0')] ).
cnf(6952,plain,
( ~ c_in(v_K,c_Message_OkeysFor(c_Message_Osynth(c_Message_Oanalz(v_H))),tc_nat)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat)
| c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Oanalz(v_H),tc_Message_Omsg) ),
inference(spr,[status(thm),theory(equality)],[6949,1]),
[iquote('0:SpR:6949.0,1.2')] ).
cnf(6954,plain,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Osynth(c_Message_Oanalz(v_H))),tc_nat),
inference(mrr,[status(thm)],[6952,447,25]),
[iquote('0:MRR:6952.1,6952.2,447.0,25.0')] ).
cnf(6971,plain,
( ~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_H)),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_nat) ),
inference(res,[status(thm),theory(equality)],[1732,6954]),
[iquote('0:Res:1732.2,6954.0')] ).
cnf(6972,plain,
$false,
inference(mrr,[status(thm)],[6971,17,445]),
[iquote('0:MRR:6971.0,6971.1,17.0,445.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV276-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 01:16:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.84/4.08
% 3.84/4.08 SPASS V 3.9
% 3.84/4.08 SPASS beiseite: Proof found.
% 3.84/4.08 % SZS status Theorem
% 3.84/4.08 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.84/4.08 SPASS derived 6302 clauses, backtracked 0 clauses, performed 0 splits and kept 4696 clauses.
% 3.84/4.08 SPASS allocated 73950 KBytes.
% 3.84/4.08 SPASS spent 0:00:03.63 on the problem.
% 3.84/4.08 0:00:00.04 for the input.
% 3.84/4.08 0:00:00.00 for the FLOTTER CNF translation.
% 3.84/4.08 0:00:00.17 for inferences.
% 3.84/4.08 0:00:00.00 for the backtracking.
% 3.84/4.08 0:00:03.33 for the reduction.
% 3.84/4.08
% 3.84/4.08
% 3.84/4.08 Here is a proof with depth 10, length 49 :
% 3.84/4.08 % SZS output start Refutation
% See solution above
% 3.84/4.08 Formulae used in the proof : cls_Event_OkeysFor__synth_H_0 cls_Event_OkeysFor__synth_H_1 cls_Message_Oanalz__conj__parts_0 cls_Message_Oanalz__subset__parts_0 cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0 cls_Message_OkeysFor__mono_0 cls_Message_OkeysFor__Un_0 cls_Message_Oparts__analz_0 cls_Message_Oparts__insert__subset__Un_0 cls_Message_Oparts__synth_0 cls_Message_Oparts__Un_0 cls_Set_OsubsetD_0 cls_Set_OUn__iff_0 cls_Set_OUn__iff_1 cls_Set_OUn__iff_2 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 3.84/4.08
%------------------------------------------------------------------------------