%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV248-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 7 unt; 4 nHn; 26 RR)
% Number of literals : 46 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 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_Oanalz(v),tc_Message_Omsg) ),
file('SWV248-2.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('SWV248-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,v,tc_Message_Omsg)
| c_in(u,c_Message_Osynth(v),tc_Message_Omsg) ),
file('SWV248-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_union(x,v,w),w) ),
file('SWV248-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(u,v,w)
| c_in(u,c_union(v,x,w),w) ),
file('SWV248-2.p',unknown),
[] ).
cnf(6,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('SWV248-2.p',unknown),
[] ).
cnf(7,axiom,
( c_lessequals(u,v,tc_set(w))
| c_in(c_Main_OsubsetI__1(u,v,w),u,w) ),
file('SWV248-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ c_in(c_Main_OsubsetI__1(u,v,w),v,w)
| c_lessequals(u,v,tc_set(w)) ),
file('SWV248-2.p',unknown),
[] ).
cnf(9,axiom,
~ c_lessequals(c_union(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Osynth(v_G),tc_Message_Omsg),c_Message_Oanalz(c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
file('SWV248-2.p',unknown),
[] ).
cnf(12,plain,
( ~ c_lessequals(c_Message_Osynth(v_G),c_Message_Oanalz(c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[6,9]),
[iquote('0:Res:6.2,9.0')] ).
cnf(14,plain,
( ~ c_in(c_Main_OsubsetI__1(u,c_Message_Oanalz(v),tc_Message_Omsg),v,tc_Message_Omsg)
| c_lessequals(u,c_Message_Oanalz(v),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[1,8]),
[iquote('0:Res:1.1,8.0')] ).
cnf(16,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)],[5,8]),
[iquote('0:Res:5.1,8.0')] ).
cnf(17,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)],[4,8]),
[iquote('0:Res:4.1,8.0')] ).
cnf(28,plain,
( ~ c_in(c_Main_OsubsetI__1(u,c_Message_Oanalz(c_union(v,w,tc_Message_Omsg)),tc_Message_Omsg),v,tc_Message_Omsg)
| c_lessequals(u,c_Message_Oanalz(c_union(v,w,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[5,14]),
[iquote('0:Res:5.1,14.0')] ).
cnf(50,plain,
( ~ c_in(c_Main_OsubsetI__1(u,c_union(c_Message_Osynth(v),w,tc_Message_Omsg),tc_Message_Omsg),v,tc_Message_Omsg)
| c_lessequals(u,c_union(c_Message_Osynth(v),w,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[3,16]),
[iquote('0:Res:3.1,16.0')] ).
cnf(64,plain,
( c_lessequals(u,c_union(v,u,w),tc_set(w))
| c_lessequals(u,c_union(v,u,w),tc_set(w)) ),
inference(res,[status(thm),theory(equality)],[7,17]),
[iquote('0:Res:7.1,17.0')] ).
cnf(67,plain,
c_lessequals(u,c_union(v,u,w),tc_set(w)),
inference(obv,[status(thm),theory(equality)],[64]),
[iquote('0:Obv:64.0')] ).
cnf(80,plain,
( ~ c_lessequals(c_union(v_G,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(v_G),c_Message_Oanalz(c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.1,12.1')] ).
cnf(137,plain,
( c_lessequals(u,c_Message_Oanalz(c_union(u,v,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| c_lessequals(u,c_Message_Oanalz(c_union(u,v,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[7,28]),
[iquote('0:Res:7.1,28.0')] ).
cnf(140,plain,
c_lessequals(u,c_Message_Oanalz(c_union(u,v,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(obv,[status(thm),theory(equality)],[137]),
[iquote('0:Obv:137.0')] ).
cnf(142,plain,
~ c_lessequals(c_union(v_G,v_H,tc_Message_Omsg),c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(mrr,[status(thm)],[80,140]),
[iquote('0:MRR:80.1,140.0')] ).
cnf(143,plain,
( ~ c_lessequals(v_G,c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_H,c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[6,142]),
[iquote('0:Res:6.2,142.0')] ).
cnf(144,plain,
~ c_lessequals(v_G,c_union(c_Message_Osynth(v_G),v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(mrr,[status(thm)],[143,67]),
[iquote('0:MRR:143.1,67.0')] ).
cnf(166,plain,
( c_lessequals(u,c_union(c_Message_Osynth(u),v,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_lessequals(u,c_union(c_Message_Osynth(u),v,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(res,[status(thm),theory(equality)],[7,50]),
[iquote('0:Res:7.1,50.0')] ).
cnf(169,plain,
c_lessequals(u,c_union(c_Message_Osynth(u),v,tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(obv,[status(thm),theory(equality)],[166]),
[iquote('0:Obv:166.0')] ).
cnf(170,plain,
$false,
inference(unc,[status(thm)],[169,144]),
[iquote('0:UnC:169.0,144.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV248-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n003.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 : Thu Jun 16 01:51:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 132 clauses, backtracked 0 clauses, performed 0 splits and kept 139 clauses.
% 0.20/0.43 SPASS allocated 63340 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.43 0:00:00.03 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.01 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 3, length 26 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : cls_Message_Oanalz_OInj_0 cls_Message_Oanalz__mono_0 cls_Message_Osynth_OInj_0 cls_Set_OUnCI_0 cls_Set_OUnCI_1 cls_Set_OUn__least_0 cls_Set_OsubsetI_0 cls_Set_OsubsetI_1 cls_conjecture_0
% 0.20/0.43
%------------------------------------------------------------------------------