TSTP Solution File: SET851-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET851-1 : 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 05:29:16 EDT 2022
% Result : Unsatisfiable 0.41s 0.59s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 9 unt; 3 nHn; 13 RR)
% Number of literals : 20 ( 0 equ; 8 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(4,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('SET851-1.p',unknown),
[] ).
cnf(6,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET851-1.p',unknown),
[] ).
cnf(7,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('SET851-1.p',unknown),
[] ).
cnf(8,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('SET851-1.p',unknown),
[] ).
cnf(9,axiom,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
file('SET851-1.p',unknown),
[] ).
cnf(10,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('SET851-1.p',unknown),
[] ).
cnf(320,axiom,
c_lessequals(u,u,tc_set(v)),
file('SET851-1.p',unknown),
[] ).
cnf(1384,plain,
( ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a)))
| equal(v_x,v_m) ),
inference(res,[status(thm),theory(equality)],[6,10]),
[iquote('0:Res:6.0,10.1')] ).
cnf(1427,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)],[4,8]),
[iquote('0:Res:4.1,8.0')] ).
cnf(1438,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(mrr,[status(thm)],[9,1427]),
[iquote('0:MRR:9.0,1427.0')] ).
cnf(1439,plain,
equal(v_x,v_m),
inference(mrr,[status(thm)],[1384,1438,7]),
[iquote('0:MRR:1384.0,1384.1,1438.0,7.0')] ).
cnf(1442,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(rew,[status(thm),theory(equality)],[1439,8]),
[iquote('0:Rew:1439.0,8.0')] ).
cnf(1454,plain,
$false,
inference(mrr,[status(thm)],[1442,320]),
[iquote('0:MRR:1442.0,320.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET851-1 : TPTP v8.1.0. Released v3.2.0.
% 0.02/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n007.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 16:38:32 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.41/0.59
% 0.41/0.59 SPASS V 3.9
% 0.41/0.59 SPASS beiseite: Proof found.
% 0.41/0.59 % SZS status Theorem
% 0.41/0.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.41/0.59 SPASS derived 40 clauses, backtracked 0 clauses, performed 0 splits and kept 1350 clauses.
% 0.41/0.59 SPASS allocated 77794 KBytes.
% 0.41/0.59 SPASS spent 0:00:00.24 on the problem.
% 0.41/0.59 0:00:00.08 for the input.
% 0.41/0.59 0:00:00.00 for the FLOTTER CNF translation.
% 0.41/0.59 0:00:00.00 for inferences.
% 0.41/0.59 0:00:00.00 for the backtracking.
% 0.41/0.59 0:00:00.07 for the reduction.
% 0.41/0.59
% 0.41/0.59
% 0.41/0.59 Here is a proof with depth 1, length 13 :
% 0.41/0.59 % SZS output start Refutation
% See solution above
% 0.41/0.59 Formulae used in the proof : cls_Zorn_Osucc__trans_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5 cls_Set_Osubset__refl_0
% 0.41/0.59
%------------------------------------------------------------------------------