TSTP Solution File: SET851-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET851-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 05:29:17 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 9 unt; 2 nHn; 13 RR)
% Number of literals : 20 ( 0 equ; 9 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; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
c_lessequals(u,u,tc_set(v)),
file('SET851-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_lessequals(u,v,tc_set(tc_set(w)))
| c_lessequals(u,c_Zorn_Osucc(x,v,w),tc_set(tc_set(w))) ),
file('SET851-2.p',unknown),
[] ).
cnf(3,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET851-2.p',unknown),
[] ).
cnf(4,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('SET851-2.p',unknown),
[] ).
cnf(5,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('SET851-2.p',unknown),
[] ).
cnf(6,axiom,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
file('SET851-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_lessequals(u,v_m,tc_set(tc_set(t_a)))
| ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| equal(u,v_m)
| c_lessequals(c_Zorn_Osucc(v_S,u,t_a),v_m,tc_set(tc_set(t_a))) ),
file('SET851-2.p',unknown),
[] ).
cnf(8,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.1,5.0')] ).
cnf(9,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(mrr,[status(thm)],[6,8]),
[iquote('0:MRR:6.1,8.0')] ).
cnf(10,plain,
( ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| equal(v_m,v_x) ),
inference(res,[status(thm),theory(equality)],[7,4]),
[iquote('0:Res:7.3,4.0')] ).
cnf(11,plain,
equal(v_m,v_x),
inference(mrr,[status(thm)],[10,9,3]),
[iquote('0:MRR:10.0,10.1,9.0,3.0')] ).
cnf(13,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(rew,[status(thm),theory(equality)],[11,5]),
[iquote('0:Rew:11.0,5.0')] ).
cnf(17,plain,
$false,
inference(mrr,[status(thm)],[13,1]),
[iquote('0:MRR:13.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET851-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.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 : Sun Jul 10 18:01:47 EDT 2022
% 0.13/0.34 % 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 8 clauses, backtracked 0 clauses, performed 0 splits and kept 13 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 1, length 13 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : cls_Set_Osubset__refl_0 cls_Zorn_Osucc__trans_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5
% 0.19/0.41
%------------------------------------------------------------------------------