TSTP Solution File: SET865-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET865-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 05:29:27 EDT 2022
% Result : Unsatisfiable 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 6 unt; 0 nHn; 17 RR)
% Number of literals : 33 ( 0 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(u,v,w)
| ~ c_lessequals(v,x,tc_set(w))
| c_in(u,x,w) ),
file('SET865-2.p',unknown),
[] ).
cnf(2,axiom,
c_in(c_Zorn_OHausdorff__1(u,v),c_Zorn_Omaxchain(u,v),tc_set(tc_set(v))),
file('SET865-2.p',unknown),
[] ).
cnf(3,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('SET865-2.p',unknown),
[] ).
cnf(4,axiom,
c_lessequals(c_Zorn_Omaxchain(u,v),c_Zorn_Ochain(u,v),tc_set(tc_set(tc_set(v)))),
file('SET865-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(u,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(u,t_a),v_S,tc_set(t_a)) ),
file('SET865-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(u,v_S,tc_set(t_a))
| c_in(v_x(u),v_S,tc_set(t_a)) ),
file('SET865-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_in(u,v_S,tc_set(t_a))
| c_lessequals(u,v_x(u),tc_set(t_a)) ),
file('SET865-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(v_x(u),u)
| ~ c_in(u,v_S,tc_set(t_a)) ),
file('SET865-2.p',unknown),
[] ).
cnf(12,plain,
( ~ c_in(u,c_Zorn_Omaxchain(v,w),tc_set(tc_set(w)))
| c_in(u,c_Zorn_Ochain(v,w),tc_set(tc_set(w))) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(14,plain,
( ~ c_in(u,v,tc_set(w))
| ~ c_lessequals(c_Union(c_Zorn_OHausdorff__1(v,w),w),u,tc_set(w))
| equal(c_Union(c_Zorn_OHausdorff__1(v,w),w),u) ),
inference(res,[status(thm),theory(equality)],[2,3]),
[iquote('0:Res:2.0,3.1')] ).
cnf(16,plain,
c_in(c_Zorn_OHausdorff__1(u,v),c_Zorn_Ochain(u,v),tc_set(tc_set(v))),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(17,plain,
c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)),
inference(res,[status(thm),theory(equality)],[16,5]),
[iquote('0:Res:16.0,5.0')] ).
cnf(18,plain,
( ~ c_in(c_Union(c_Zorn_OHausdorff__1(u,t_a),t_a),v_S,tc_set(t_a))
| ~ c_in(v_x(c_Union(c_Zorn_OHausdorff__1(u,t_a),t_a)),u,tc_set(t_a))
| equal(v_x(c_Union(c_Zorn_OHausdorff__1(u,t_a),t_a)),c_Union(c_Zorn_OHausdorff__1(u,t_a),t_a)) ),
inference(res,[status(thm),theory(equality)],[7,14]),
[iquote('0:Res:7.1,14.1')] ).
cnf(19,plain,
( ~ c_in(c_Union(c_Zorn_OHausdorff__1(u,t_a),t_a),v_S,tc_set(t_a))
| ~ c_in(v_x(c_Union(c_Zorn_OHausdorff__1(u,t_a),t_a)),u,tc_set(t_a)) ),
inference(mrr,[status(thm)],[18,8]),
[iquote('0:MRR:18.2,8.0')] ).
cnf(24,plain,
( ~ c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a))
| ~ c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)) ),
inference(res,[status(thm),theory(equality)],[6,19]),
[iquote('0:Res:6.1,19.1')] ).
cnf(25,plain,
~ c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)),
inference(obv,[status(thm),theory(equality)],[24]),
[iquote('0:Obv:24.0')] ).
cnf(26,plain,
$false,
inference(mrr,[status(thm)],[25,17]),
[iquote('0:MRR:25.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET865-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sat Jul 9 17:46:31 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.21/0.43
% 0.21/0.43 SPASS V 3.9
% 0.21/0.43 SPASS beiseite: Proof found.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.43 SPASS derived 15 clauses, backtracked 0 clauses, performed 0 splits and kept 23 clauses.
% 0.21/0.43 SPASS allocated 63119 KBytes.
% 0.21/0.43 SPASS spent 0:00:00.06 on the problem.
% 0.21/0.43 0:00:00.04 for the input.
% 0.21/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.43 0:00:00.00 for inferences.
% 0.21/0.43 0:00:00.00 for the backtracking.
% 0.21/0.43 0:00:00.00 for the reduction.
% 0.21/0.43
% 0.21/0.43
% 0.21/0.43 Here is a proof with depth 3, length 17 :
% 0.21/0.43 % SZS output start Refutation
% See solution above
% 0.21/0.43 Formulae used in the proof : cls_Set_OsubsetD_0 cls_Zorn_OHausdorff_0 cls_Zorn_Omaxchain__Zorn_0 cls_Zorn_Omaxchain__subset__chain_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.21/0.43
%------------------------------------------------------------------------------