%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV251-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 21:41:49 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 9 unt; 0 nHn; 18 RR)
% Number of literals : 28 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,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('SWV251-2.p',unknown),
[] ).
cnf(3,axiom,
equal(c_union(u,c_minus(v,u,tc_set(w)),w),c_union(u,v,w)),
file('SWV251-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_lessequals(c_union(u,v,w),x,tc_set(w))
| c_lessequals(v,x,tc_set(w)) ),
file('SWV251-2.p',unknown),
[] ).
cnf(7,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('SWV251-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ c_in(u,v,w)
| ~ c_lessequals(v,x,tc_set(w))
| c_in(u,x,w) ),
file('SWV251-2.p',unknown),
[] ).
cnf(10,axiom,
c_lessequals(u,u,tc_set(v)),
file('SWV251-2.p',unknown),
[] ).
cnf(11,axiom,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
file('SWV251-2.p',unknown),
[] ).
cnf(12,axiom,
c_in(v_x,c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),tc_Message_Omsg),
file('SWV251-2.p',unknown),
[] ).
cnf(13,axiom,
~ c_in(v_x,c_Message_Oanalz(c_union(c_Message_Osynth(c_Message_Oanalz(v_G)),v_H,tc_Message_Omsg)),tc_Message_Omsg),
file('SWV251-2.p',unknown),
[] ).
cnf(17,plain,
( ~ c_lessequals(c_Message_Oanalz(c_insert(v_X,v_H,tc_Message_Omsg)),u,tc_set(tc_Message_Omsg))
| c_in(v_x,u,tc_Message_Omsg) ),
inference(res,[status(thm),theory(equality)],[12,8]),
[iquote('0:Res:12.0,8.0')] ).
cnf(25,plain,
( ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),u,tc_set(tc_Message_Omsg))
| c_in(v_x,c_Message_Oanalz(u),tc_Message_Omsg) ),
inference(res,[status(thm),theory(equality)],[1,17]),
[iquote('0:Res:1.1,17.0')] ).
cnf(28,plain,
c_lessequals(u,c_union(v,u,w),tc_set(w)),
inference(res,[status(thm),theory(equality)],[10,5]),
[iquote('0:Res:10.0,5.0')] ).
cnf(112,plain,
( ~ c_in(u,v,w)
| equal(c_union(v,c_minus(x,v,tc_set(w)),w),c_union(v,c_insert(u,x,w),w)) ),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.1,3.0')] ).
cnf(113,plain,
( ~ c_in(u,v,w)
| equal(c_union(v,c_insert(u,x,w),w),c_union(v,x,w)) ),
inference(rew,[status(thm),theory(equality)],[3,112]),
[iquote('0:Rew:3.0,112.1')] ).
cnf(122,plain,
c_in(v_x,c_Message_Oanalz(c_union(u,c_insert(v_X,v_H,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
inference(res,[status(thm),theory(equality)],[28,25]),
[iquote('0:Res:28.0,25.0')] ).
cnf(175,plain,
( ~ c_in(v_X,u,tc_Message_Omsg)
| c_in(v_x,c_Message_Oanalz(c_union(u,v_H,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(spr,[status(thm),theory(equality)],[113,122]),
[iquote('0:SpR:113.1,122.0')] ).
cnf(212,plain,
~ c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_G)),tc_Message_Omsg),
inference(res,[status(thm),theory(equality)],[175,13]),
[iquote('0:Res:175.1,13.0')] ).
cnf(213,plain,
$false,
inference(mrr,[status(thm)],[212,11]),
[iquote('0:MRR:212.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV251-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.33 % CPULimit : 300
% 0.19/0.33 % WCLimit : 600
% 0.19/0.33 % DateTime : Wed Jun 15 03:52:33 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 193 clauses, backtracked 0 clauses, performed 0 splits and kept 116 clauses.
% 0.19/0.43 SPASS allocated 63390 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.43 0:00:00.03 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.01 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.02 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 5, length 18 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : cls_Message_Oanalz__mono_0 cls_Set_OUn__Diff__cancel_0 cls_Set_OUn__subset__iff_1 cls_Set_Oinsert__Diff1_0 cls_Set_OsubsetD_0 cls_Set_Osubset__refl_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2
% 0.19/0.43
%------------------------------------------------------------------------------