TSTP Solution File: SET864-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET864-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 : Tue Jul 19 05:29:26 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 6 unt; 0 nHn; 12 RR)
% Number of literals : 22 ( 0 equ; 14 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(u,v,tc_set(w))
| ~ c_in(x,c_Zorn_Omaxchain(v,w),tc_set(tc_set(w)))
| ~ c_lessequals(c_Union(x,w),u,tc_set(w))
| equal(c_Union(x,w),u) ),
file('SET864-2.p',unknown),
[] ).
cnf(2,axiom,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('SET864-2.p',unknown),
[] ).
cnf(3,axiom,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
file('SET864-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,v_S,tc_set(t_a))
| c_in(v_x(u),v_S,tc_set(t_a)) ),
file('SET864-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(u,v_S,tc_set(t_a))
| c_lessequals(u,v_x(u),tc_set(t_a)) ),
file('SET864-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(v_x(u),u)
| ~ c_in(u,v_S,tc_set(t_a)) ),
file('SET864-2.p',unknown),
[] ).
cnf(7,plain,
~ equal(v_x(c_Union(v_c,t_a)),c_Union(v_c,t_a)),
inference(res,[status(thm),theory(equality)],[3,6]),
[iquote('0:Res:3.0,6.1')] ).
cnf(13,plain,
( ~ c_in(u,v_S,tc_set(t_a))
| ~ c_lessequals(c_Union(v_c,t_a),u,tc_set(t_a))
| equal(c_Union(v_c,t_a),u) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(14,plain,
( ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| ~ c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a))
| equal(v_x(c_Union(v_c,t_a)),c_Union(v_c,t_a)) ),
inference(res,[status(thm),theory(equality)],[5,13]),
[iquote('0:Res:5.1,13.1')] ).
cnf(15,plain,
~ c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)),
inference(mrr,[status(thm)],[14,3,7]),
[iquote('0:MRR:14.0,14.2,3.0,7.0')] ).
cnf(16,plain,
~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
inference(res,[status(thm),theory(equality)],[4,15]),
[iquote('0:Res:4.1,15.0')] ).
cnf(17,plain,
$false,
inference(mrr,[status(thm)],[16,3]),
[iquote('0:MRR:16.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET864-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 02:32:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 15 clauses.
% 0.19/0.41 SPASS allocated 63097 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.04 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 3, length 12 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : cls_Zorn_Omaxchain__Zorn_0 cls_conjecture_0 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5
% 0.19/0.41
%------------------------------------------------------------------------------