TSTP Solution File: SWV339-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV339-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 21:42:22 EDT 2022
% Result : Unsatisfiable 2.41s 2.58s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 21 unt; 4 nHn; 27 RR)
% Number of literals : 39 ( 0 equ; 13 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 13 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
c_in(v_K,c_Message_OsymKeys,tc_nat),
file('SWV339-1.p',unknown),
[] ).
cnf(8,axiom,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
file('SWV339-1.p',unknown),
[] ).
cnf(10,axiom,
( equal(c_Public_OshrK(v_A),v_K)
| equal(c_Public_OshrK(v_B),v_K) ),
file('SWV339-1.p',unknown),
[] ).
cnf(253,axiom,
class_Orderings_Olinorder(tc_nat),
file('SWV339-1.p',unknown),
[] ).
cnf(1284,axiom,
( ~ class_Orderings_Olinorder(u)
| ~ c_in(v,w,u)
| ~ c_in(w,c_Finite__Set_OFinites,tc_set(u))
| equal(w,c_emptyset)
| c_lessequals(c_Finite__Set_OMin(w,u),v,u) ),
file('SWV339-1.p',unknown),
[] ).
cnf(2600,axiom,
equal(c_minus(u,c_emptyset,tc_set(v)),u),
file('SWV339-1.p',unknown),
[] ).
cnf(2684,axiom,
( ~ c_in(u,v,w)
| equal(c_minus(c_insert(u,x,w),v,tc_set(w)),c_minus(x,v,tc_set(w))) ),
file('SWV339-1.p',unknown),
[] ).
cnf(2697,axiom,
~ equal(c_insert(u,v,w),c_emptyset),
file('SWV339-1.p',unknown),
[] ).
cnf(2936,axiom,
c_in(c_Message_Omsg_OKey(c_Public_OshrK(u)),c_Event_Oused(v),tc_Message_Omsg),
file('SWV339-1.p',unknown),
[] ).
cnf(3353,plain,
equal(c_minus(c_insert(v_K,u,tc_nat),c_Message_OsymKeys,tc_set(tc_nat)),c_minus(u,c_Message_OsymKeys,tc_set(tc_nat))),
inference(res,[status(thm),theory(equality)],[2,2684]),
[iquote('0:Res:2.0,2684.0')] ).
cnf(3377,plain,
( ~ class_Orderings_Olinorder(tc_nat)
| ~ c_in(c_Message_OsymKeys,c_Finite__Set_OFinites,tc_set(tc_nat))
| c_lessequals(c_Finite__Set_OMin(c_Message_OsymKeys,tc_nat),v_K,tc_nat)
| equal(c_emptyset,c_Message_OsymKeys) ),
inference(res,[status(thm),theory(equality)],[2,1284]),
[iquote('0:Res:2.0,1284.1')] ).
cnf(3517,plain,
( ~ c_in(c_Message_OsymKeys,c_Finite__Set_OFinites,tc_set(tc_nat))
| equal(c_emptyset,c_Message_OsymKeys)
| c_lessequals(c_Finite__Set_OMin(c_Message_OsymKeys,tc_nat),v_K,tc_nat) ),
inference(mrr,[status(thm)],[3377,253]),
[iquote('0:MRR:3377.0,253.0')] ).
cnf(3564,plain,
equal(c_emptyset,c_Message_OsymKeys),
inference(spt,[spt(split,[position(s1)])],[3517]),
[iquote('1:Spt:3517.1')] ).
cnf(3657,plain,
~ equal(c_insert(u,v,w),c_Message_OsymKeys),
inference(rew,[status(thm),theory(equality)],[3564,2697]),
[iquote('1:Rew:3564.0,2697.0')] ).
cnf(3659,plain,
equal(c_minus(u,c_Message_OsymKeys,tc_set(v)),u),
inference(rew,[status(thm),theory(equality)],[3564,2600]),
[iquote('1:Rew:3564.0,2600.0')] ).
cnf(3716,plain,
equal(c_minus(u,c_Message_OsymKeys,tc_set(tc_nat)),c_insert(v_K,u,tc_nat)),
inference(rew,[status(thm),theory(equality)],[3659,3353]),
[iquote('1:Rew:3659.0,3353.0')] ).
cnf(3741,plain,
equal(c_insert(v_K,u,tc_nat),u),
inference(rew,[status(thm),theory(equality)],[3659,3716]),
[iquote('1:Rew:3659.0,3716.0')] ).
cnf(3742,plain,
$false,
inference(unc,[status(thm)],[3741,3657]),
[iquote('1:UnC:3741.0,3657.0')] ).
cnf(3752,plain,
~ equal(c_emptyset,c_Message_OsymKeys),
inference(spt,[spt(split,[position(sa)])],[3742,3564]),
[iquote('1:Spt:3742.0,3517.1,3564.0')] ).
cnf(3753,plain,
( ~ c_in(c_Message_OsymKeys,c_Finite__Set_OFinites,tc_set(tc_nat))
| c_lessequals(c_Finite__Set_OMin(c_Message_OsymKeys,tc_nat),v_K,tc_nat) ),
inference(spt,[spt(split,[position(s2)])],[3517]),
[iquote('1:Spt:3742.0,3517.0,3517.2')] ).
cnf(3770,plain,
equal(c_Public_OshrK(v_B),v_K),
inference(spt,[spt(split,[position(s2s1)])],[10]),
[iquote('2:Spt:10.1')] ).
cnf(4062,plain,
c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(u),tc_Message_Omsg),
inference(spr,[status(thm),theory(equality)],[3770,2936]),
[iquote('2:SpR:3770.0,2936.0')] ).
cnf(4063,plain,
$false,
inference(unc,[status(thm)],[4062,8]),
[iquote('2:UnC:4062.0,8.0')] ).
cnf(4064,plain,
~ equal(c_Public_OshrK(v_B),v_K),
inference(spt,[spt(split,[position(s2sa)])],[4063,3770]),
[iquote('2:Spt:4063.0,10.1,3770.0')] ).
cnf(4065,plain,
equal(c_Public_OshrK(v_A),v_K),
inference(spt,[spt(split,[position(s2s2)])],[10]),
[iquote('2:Spt:4063.0,10.0')] ).
cnf(4069,plain,
c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(u),tc_Message_Omsg),
inference(spr,[status(thm),theory(equality)],[4065,2936]),
[iquote('2:SpR:4065.0,2936.0')] ).
cnf(4071,plain,
$false,
inference(unc,[status(thm)],[4069,8]),
[iquote('2:UnC:4069.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV339-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 15 11:36:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.41/2.58
% 2.41/2.58 SPASS V 3.9
% 2.41/2.58 SPASS beiseite: Proof found.
% 2.41/2.58 % SZS status Theorem
% 2.41/2.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.41/2.58 SPASS derived 752 clauses, backtracked 187 clauses, performed 3 splits and kept 3360 clauses.
% 2.41/2.58 SPASS allocated 81151 KBytes.
% 2.41/2.58 SPASS spent 0:00:02.16 on the problem.
% 2.41/2.58 0:00:00.23 for the input.
% 2.41/2.58 0:00:00.00 for the FLOTTER CNF translation.
% 2.41/2.58 0:00:00.03 for inferences.
% 2.41/2.58 0:00:00.01 for the backtracking.
% 2.41/2.58 0:00:01.14 for the reduction.
% 2.41/2.58
% 2.41/2.58
% 2.41/2.58 Here is a proof with depth 2, length 27 :
% 2.41/2.58 % SZS output start Refutation
% See solution above
% 2.41/2.58 Formulae used in the proof : cls_conjecture_0 cls_conjecture_6 cls_conjecture_8 clsarity_nat_7 cls_Finite__Set_OMin__le_0 cls_Set_ODiff__empty_0 cls_Set_Oinsert__Diff1_0 cls_Set_Oinsert__not__empty_0 cls_Public_OshrK__in__used_0
% 2.41/2.58
%------------------------------------------------------------------------------