TSTP Solution File: SET864-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET864-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 4.06s 4.27s
% Output : Refutation 4.06s
% 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(2,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('SET864-1.p',unknown),
[] ).
cnf(4,axiom,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('SET864-1.p',unknown),
[] ).
cnf(6,axiom,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
file('SET864-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_in(u,v_S,tc_set(t_a))
| c_in(v_x(u),v_S,tc_set(t_a)) ),
file('SET864-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ c_in(u,v_S,tc_set(t_a))
| c_lessequals(u,v_x(u),tc_set(t_a)) ),
file('SET864-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(v_x(u),u)
| ~ c_in(u,v_S,tc_set(t_a)) ),
file('SET864-1.p',unknown),
[] ).
cnf(1426,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)],[4,2]),
[iquote('0:Res:4.0,2.1')] ).
cnf(1514,plain,
~ equal(v_x(c_Union(v_c,t_a)),c_Union(v_c,t_a)),
inference(res,[status(thm),theory(equality)],[6,9]),
[iquote('0:Res:6.0,9.1')] ).
cnf(8064,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)],[8,1426]),
[iquote('0:Res:8.1,1426.1')] ).
cnf(8067,plain,
~ c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)),
inference(mrr,[status(thm)],[8064,6,1514]),
[iquote('0:MRR:8064.0,8064.2,6.0,1514.0')] ).
cnf(8069,plain,
~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
inference(res,[status(thm),theory(equality)],[7,8067]),
[iquote('0:Res:7.1,8067.0')] ).
cnf(8070,plain,
$false,
inference(mrr,[status(thm)],[8069,6]),
[iquote('0:MRR:8069.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET864-1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n017.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 : Mon Jul 11 04:43:03 EDT 2022
% 0.12/0.35 % CPUTime :
% 4.06/4.27
% 4.06/4.27 SPASS V 3.9
% 4.06/4.27 SPASS beiseite: Proof found.
% 4.06/4.27 % SZS status Theorem
% 4.06/4.27 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.06/4.27 SPASS derived 5657 clauses, backtracked 22 clauses, performed 2 splits and kept 4224 clauses.
% 4.06/4.27 SPASS allocated 88365 KBytes.
% 4.06/4.27 SPASS spent 0:00:03.74 on the problem.
% 4.06/4.27 0:00:00.08 for the input.
% 4.06/4.27 0:00:00.00 for the FLOTTER CNF translation.
% 4.06/4.27 0:00:00.20 for inferences.
% 4.06/4.27 0:00:00.00 for the backtracking.
% 4.06/4.27 0:00:03.14 for the reduction.
% 4.06/4.27
% 4.06/4.27
% 4.06/4.27 Here is a proof with depth 3, length 12 :
% 4.06/4.27 % SZS output start Refutation
% See solution above
% 4.06/4.27 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
% 4.06/4.27
%------------------------------------------------------------------------------