TSTP Solution File: SET841-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET841-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 05:29:09 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 12 ( 10 unt; 1 nHn; 12 RR)
% Number of literals : 19 ( 0 equ; 9 neg)
% Maximal clause size : 5 ( 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(1,axiom,
c_lessequals(u,u,tc_set(v)),
file('SET841-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_lessequals(u,v,tc_set(tc_set(w)))
| ~ c_in(v,c_Zorn_OTFin(x,w),tc_set(tc_set(w)))
| ~ c_in(u,c_Zorn_OTFin(x,w),tc_set(tc_set(w)))
| equal(u,v)
| c_lessequals(c_Zorn_Osucc(x,u,w),v,tc_set(tc_set(w))) ),
file('SET841-2.p',unknown),
[] ).
cnf(3,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET841-2.p',unknown),
[] ).
cnf(4,axiom,
equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m),
file('SET841-2.p',unknown),
[] ).
cnf(5,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET841-2.p',unknown),
[] ).
cnf(6,axiom,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
file('SET841-2.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('SET841-2.p',unknown),
[] ).
cnf(13,plain,
( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| equal(v_x,v_m) ),
inference(res,[status(thm),theory(equality)],[2,7]),
[iquote('0:Res:2.3,7.0')] ).
cnf(14,plain,
equal(v_x,v_m),
inference(mrr,[status(thm)],[13,5,3,6]),
[iquote('0:MRR:13.0,13.1,13.2,5.0,3.0,6.0')] ).
cnf(17,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
inference(rew,[status(thm),theory(equality)],[14,7]),
[iquote('0:Rew:14.0,7.0')] ).
cnf(18,plain,
~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a))),
inference(rew,[status(thm),theory(equality)],[4,17]),
[iquote('0:Rew:4.0,17.0')] ).
cnf(19,plain,
$false,
inference(mrr,[status(thm)],[18,1]),
[iquote('0:MRR:18.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET841-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 : Sun Jul 10 01:30:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 9 clauses.
% 0.19/0.42 SPASS allocated 63104 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.00 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 1, length 12 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : cls_Set_Osubset__refl_0 cls_Zorn_OTFin__subsetD_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4
% 0.19/0.42
%------------------------------------------------------------------------------