TSTP Solution File: SET852-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET852-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 0.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 3 unt; 9 nHn; 12 RR)
% Number of literals : 33 ( 0 equ; 8 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( c_lessequals(u,c_Union(v,w),tc_set(w))
| c_lessequals(c_Union(v,w),x,tc_set(w))
| c_in(c_Zorn_OUnion__lemma0__1(x,u,v,w),v,tc_set(w)) ),
file('SET852-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(u,v,w,x),u,tc_set(x))
| c_lessequals(v,c_Union(w,x),tc_set(x))
| c_lessequals(c_Union(w,x),u,tc_set(x)) ),
file('SET852-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_lessequals(u,c_Zorn_OUnion__lemma0__1(v,u,w,x),tc_set(x))
| c_lessequals(u,c_Union(w,x),tc_set(x))
| c_lessequals(c_Union(w,x),v,tc_set(x)) ),
file('SET852-2.p',unknown),
[] ).
cnf(4,axiom,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('SET852-2.p',unknown),
[] ).
cnf(5,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('SET852-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(u,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(u,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),u,tc_set(tc_set(t_a))) ),
file('SET852-2.p',unknown),
[] ).
cnf(9,plain,
( ~ c_in(c_Zorn_OUnion__lemma0__1(u,c_Zorn_Osucc(v_S,v_m,t_a),v,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(u,c_Zorn_Osucc(v_S,v_m,t_a),v,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v,tc_set(t_a)),u,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[6,3]),
[iquote('0:Res:6.2,3.0')] ).
cnf(10,plain,
( ~ c_in(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),u,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(u,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(u,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(u,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(u,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[9,2]),
[iquote('0:Res:9.1,2.0')] ).
cnf(11,plain,
( ~ c_in(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),u,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(u,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(u,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(obv,[status(thm),theory(equality)],[10]),
[iquote('0:Obv:10.2')] ).
cnf(12,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.2,11.0')] ).
cnf(13,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(obv,[status(thm),theory(equality)],[12]),
[iquote('0:Obv:12.1')] ).
cnf(14,plain,
$false,
inference(mrr,[status(thm)],[13,5,4]),
[iquote('0:MRR:13.0,13.1,5.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET852-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n012.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 05:20:28 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.40
% 0.19/0.40 SPASS V 3.9
% 0.19/0.40 SPASS beiseite: Proof found.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.40 SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 10 clauses.
% 0.19/0.40 SPASS allocated 63106 KBytes.
% 0.19/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.40 0:00:00.03 for the input.
% 0.19/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40 0:00:00.00 for inferences.
% 0.19/0.40 0:00:00.00 for the backtracking.
% 0.19/0.40 0:00:00.00 for the reduction.
% 0.19/0.40
% 0.19/0.40
% 0.19/0.40 Here is a proof with depth 3, length 12 :
% 0.19/0.40 % SZS output start Refutation
% See solution above
% 0.19/0.40 Formulae used in the proof : cls_Zorn_OUnion__lemma0_0 cls_Zorn_OUnion__lemma0_1 cls_Zorn_OUnion__lemma0_2 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4
% 0.19/0.40
%------------------------------------------------------------------------------