TSTP Solution File: SET850-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET850-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 05:29:15 EDT 2022
% Result : Unsatisfiable 0.39s 0.59s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 7 RR)
% Number of literals : 10 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_lessequals(u,v,tc_set(w))
| ~ c_lessequals(v,x,tc_set(w))
| c_lessequals(u,x,tc_set(w)) ),
file('SET850-1.p',unknown),
[] ).
cnf(2,axiom,
c_lessequals(u,c_Zorn_Osucc(v,u,w),tc_set(tc_set(w))),
file('SET850-1.p',unknown),
[] ).
cnf(3,axiom,
c_lessequals(v_x,v_y,tc_set(tc_set(t_a))),
file('SET850-1.p',unknown),
[] ).
cnf(4,axiom,
~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(tc_set(t_a))),
file('SET850-1.p',unknown),
[] ).
cnf(1378,plain,
( ~ c_lessequals(u,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,u,tc_set(tc_set(t_a))) ),
inference(res,[status(thm),theory(equality)],[1,4]),
[iquote('0:Res:1.2,4.0')] ).
cnf(1390,plain,
~ c_lessequals(v_y,c_Zorn_Osucc(v_S,v_y,t_a),tc_set(tc_set(t_a))),
inference(res,[status(thm),theory(equality)],[3,1378]),
[iquote('0:Res:3.0,1378.1')] ).
cnf(1392,plain,
$false,
inference(mrr,[status(thm)],[1390,2]),
[iquote('0:MRR:1390.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET850-1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n024.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 15:54:28 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.39/0.59
% 0.39/0.59 SPASS V 3.9
% 0.39/0.59 SPASS beiseite: Proof found.
% 0.39/0.59 % SZS status Theorem
% 0.39/0.59 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.59 SPASS derived 15 clauses, backtracked 0 clauses, performed 0 splits and kept 1340 clauses.
% 0.39/0.59 SPASS allocated 77780 KBytes.
% 0.39/0.59 SPASS spent 0:00:00.24 on the problem.
% 0.39/0.59 0:00:00.08 for the input.
% 0.39/0.59 0:00:00.00 for the FLOTTER CNF translation.
% 0.39/0.59 0:00:00.00 for inferences.
% 0.39/0.59 0:00:00.00 for the backtracking.
% 0.39/0.59 0:00:00.07 for the reduction.
% 0.39/0.59
% 0.39/0.59
% 0.39/0.59 Here is a proof with depth 2, length 7 :
% 0.39/0.59 % SZS output start Refutation
% See solution above
% 0.39/0.59 Formulae used in the proof : cls_Set_Osubset__trans_0 cls_Zorn_OAbrial__axiom1_0 cls_conjecture_0 cls_conjecture_1
% 0.39/0.59
%------------------------------------------------------------------------------