TSTP Solution File: SET848-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET848-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 05:29:14 EDT 2022
% Result : Unsatisfiable 0.12s 0.41s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 8 unt; 1 nHn; 13 RR)
% Number of literals : 19 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(u,v,w)
| c_in(u,x,w)
| c_in(u,c_minus(v,x,tc_set(w)),w) ),
file('SET848-2.p',unknown),
[] ).
cnf(2,axiom,
c_lessequals(u,u,tc_set(v)),
file('SET848-2.p',unknown),
[] ).
cnf(3,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('SET848-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
| c_in(u,c_Zorn_Ochain(v,w),tc_set(tc_set(w))) ),
file('SET848-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(c_Zorn_Osucc(u,v,w),v)
| ~ c_in(v,c_minus(c_Zorn_Ochain(u,w),c_Zorn_Omaxchain(u,w),tc_set(tc_set(tc_set(w)))),tc_set(tc_set(w))) ),
file('SET848-2.p',unknown),
[] ).
cnf(6,axiom,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('SET848-2.p',unknown),
[] ).
cnf(7,axiom,
equal(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))),
file('SET848-2.p',unknown),
[] ).
cnf(9,plain,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_minus(c_Zorn_Ochain(v_S,t_a),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[7,5]),
[iquote('0:Res:7.0,5.1')] ).
cnf(11,plain,
( ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.2,9.0')] ).
cnf(12,plain,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(mrr,[status(thm)],[11,6]),
[iquote('0:MRR:11.1,6.0')] ).
cnf(13,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)],[4,12]),
[iquote('0:Res:4.1,12.0')] ).
cnf(14,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)],[3,13]),
[iquote('0:Res:3.1,13.0')] ).
cnf(15,plain,
$false,
inference(mrr,[status(thm)],[14,2]),
[iquote('0:MRR:14.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET848-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n008.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 : Sun Jul 10 06:59:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.41
% 0.12/0.41 SPASS V 3.9
% 0.12/0.41 SPASS beiseite: Proof found.
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41 SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 11 clauses.
% 0.12/0.41 SPASS allocated 63104 KBytes.
% 0.12/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.12/0.41 0:00:00.03 for the input.
% 0.12/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.41 0:00:00.00 for inferences.
% 0.12/0.41 0:00:00.00 for the backtracking.
% 0.12/0.41 0:00:00.00 for the reduction.
% 0.12/0.41
% 0.12/0.41
% 0.12/0.41 Here is a proof with depth 4, length 13 :
% 0.12/0.41 % SZS output start Refutation
% See solution above
% 0.12/0.41 Formulae used in the proof : cls_Set_ODiffI_0 cls_Set_Osubset__refl_0 cls_Zorn_OTFin__UnionI_0 cls_Zorn_OTFin__chain__lemma4_0 cls_Zorn_Osucc__not__equals_0 cls_conjecture_0 cls_conjecture_1
% 0.12/0.41
%------------------------------------------------------------------------------