TSTP Solution File: SET846-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET846-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 05:29:13 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 9 RR)
% Number of literals : 12 ( 0 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(u,v,tc_set(w))
| c_lessequals(u,c_Union(v,w),tc_set(w)) ),
file('SET846-2.p',unknown),
[] ).
cnf(2,axiom,
c_lessequals(u,u,tc_set(v)),
file('SET846-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| c_in(c_Zorn_Osucc(v,u,w),c_Zorn_OTFin(v,w),tc_set(tc_set(w))) ),
file('SET846-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_lessequals(u,c_Zorn_OTFin(v,w),tc_set(tc_set(tc_set(w))))
| c_in(c_Union(u,tc_set(w)),c_Zorn_OTFin(v,w),tc_set(tc_set(w))) ),
file('SET846-2.p',unknown),
[] ).
cnf(5,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
file('SET846-2.p',unknown),
[] ).
cnf(6,plain,
~ c_in(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[1,5]),
[iquote('0:Res:1.1,5.0')] ).
cnf(8,plain,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[3,6]),
[iquote('0:Res:3.1,6.0')] ).
cnf(9,plain,
~ c_lessequals(c_Zorn_OTFin(v_S,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
inference(res,[status(thm),theory(equality)],[4,8]),
[iquote('0:Res:4.1,8.0')] ).
cnf(10,plain,
$false,
inference(mrr,[status(thm)],[9,2]),
[iquote('0:MRR:9.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET846-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n003.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 04:12:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.39
% 0.12/0.39 SPASS V 3.9
% 0.12/0.39 SPASS beiseite: Proof found.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.39 SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 8 clauses.
% 0.12/0.39 SPASS allocated 63094 KBytes.
% 0.12/0.39 SPASS spent 0:00:00.04 on the problem.
% 0.12/0.39 0:00:00.03 for the input.
% 0.12/0.39 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.39 0:00:00.00 for inferences.
% 0.12/0.39 0:00:00.00 for the backtracking.
% 0.12/0.39 0:00:00.00 for the reduction.
% 0.12/0.39
% 0.12/0.39
% 0.12/0.39 Here is a proof with depth 3, length 9 :
% 0.12/0.39 % SZS output start Refutation
% See solution above
% 0.12/0.39 Formulae used in the proof : cls_Set_OUnion__upper_0 cls_Set_Osubset__refl_0 cls_Zorn_OTFin_OsuccI_0 cls_Zorn_OTFin__UnionI_0 cls_conjecture_1
% 0.12/0.39
%------------------------------------------------------------------------------