TSTP Solution File: SET852-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET852-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 1.05s 1.28s
% Output : Refutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 14 ( 6 unt; 5 nHn; 14 RR)
% Number of literals : 26 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 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('SET852-1.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('SET852-1.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('SET852-1.p',unknown),
[] ).
cnf(7,axiom,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('SET852-1.p',unknown),
[] ).
cnf(8,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('SET852-1.p',unknown),
[] ).
cnf(9,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('SET852-1.p',unknown),
[] ).
cnf(1430,plain,
( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(u,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),u,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),u,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[2,8]),
[iquote('0:Res:2.1,8.0')] ).
cnf(1431,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),u,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OUnion__lemma0__1(u,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[1,8]),
[iquote('0:Res:1.1,8.0')] ).
cnf(1432,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(u,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),u,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[3,8]),
[iquote('0:Res:3.1,8.0')] ).
cnf(1442,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[1432,7]),
[iquote('0:Res:1432.1,7.0')] ).
cnf(1443,plain,
~ c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[1430,7]),
[iquote('0:Res:1430.1,7.0')] ).
cnf(1444,plain,
c_in(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[1431,7]),
[iquote('0:Res:1431.1,7.0')] ).
cnf(3318,plain,
( ~ c_in(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[9,1442]),
[iquote('0:Res:9.2,1442.0')] ).
cnf(3323,plain,
$false,
inference(mrr,[status(thm)],[3318,1444,1443]),
[iquote('0:MRR:3318.0,3318.1,1444.0,1443.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET852-1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n014.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 : Mon Jul 11 03:23:04 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.05/1.28
% 1.05/1.28 SPASS V 3.9
% 1.05/1.28 SPASS beiseite: Proof found.
% 1.05/1.28 % SZS status Theorem
% 1.05/1.28 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.05/1.28 SPASS derived 1669 clauses, backtracked 0 clauses, performed 2 splits and kept 2131 clauses.
% 1.05/1.28 SPASS allocated 80104 KBytes.
% 1.05/1.28 SPASS spent 0:00:00.89 on the problem.
% 1.05/1.28 0:00:00.08 for the input.
% 1.05/1.28 0:00:00.00 for the FLOTTER CNF translation.
% 1.05/1.28 0:00:00.07 for inferences.
% 1.05/1.28 0:00:00.01 for the backtracking.
% 1.05/1.28 0:00:00.49 for the reduction.
% 1.05/1.28
% 1.05/1.28
% 1.05/1.28 Here is a proof with depth 3, length 14 :
% 1.05/1.28 % SZS output start Refutation
% See solution above
% 1.05/1.28 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
% 1.05/1.28
%------------------------------------------------------------------------------