TSTP Solution File: SET858-2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET858-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 05:29:21 EDT 2022

% Result   : Unsatisfiable 0.18s 0.49s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   19 (   6 unt;  11 nHn;  19 RR)
%            Number of literals    :   64 (   0 equ;  32 neg)
%            Maximal clause size   :    8 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 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('SET858-2.p',unknown),
    [] ).

cnf(2,axiom,
    c_lessequals(u,c_Zorn_Osucc(v,u,w),tc_set(tc_set(w))),
    file('SET858-2.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
    | ~ c_in(x,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
    | c_lessequals(u,x,tc_set(tc_set(w)))
    | c_lessequals(c_Zorn_Osucc(v,x,w),u,tc_set(tc_set(w)))
    | c_in(c_Zorn_OTFin__linear__lemma1__1(v,x,w),c_Zorn_OTFin(v,w),tc_set(tc_set(w))) ),
    file('SET858-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
    | ~ c_in(x,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
    | c_lessequals(u,x,tc_set(tc_set(w)))
    | c_lessequals(c_Zorn_Osucc(v,x,w),u,tc_set(tc_set(w)))
    | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v,x,w),x,tc_set(tc_set(w))) ),
    file('SET858-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ equal(c_Zorn_OTFin__linear__lemma1__1(u,v,w),v)
    | ~ c_in(x,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
    | ~ c_in(v,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
    | c_lessequals(x,v,tc_set(tc_set(w)))
    | c_lessequals(c_Zorn_Osucc(u,v,w),x,tc_set(tc_set(w))) ),
    file('SET858-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
    | ~ c_in(x,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
    | ~ c_lessequals(c_Zorn_Osucc(v,c_Zorn_OTFin__linear__lemma1__1(v,x,w),w),x,tc_set(tc_set(w)))
    | c_lessequals(u,x,tc_set(tc_set(w)))
    | c_lessequals(c_Zorn_Osucc(v,x,w),u,tc_set(tc_set(w))) ),
    file('SET858-2.p',unknown),
    [] ).

cnf(7,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('SET858-2.p',unknown),
    [] ).

cnf(8,axiom,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('SET858-2.p',unknown),
    [] ).

cnf(9,axiom,
    c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('SET858-2.p',unknown),
    [] ).

cnf(10,axiom,
    ~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
    file('SET858-2.p',unknown),
    [] ).

cnf(11,axiom,
    ~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
    file('SET858-2.p',unknown),
    [] ).

cnf(42,plain,
    ( ~ c_lessequals(c_Zorn_Osucc(u,v,w),x,tc_set(tc_set(w)))
    | c_lessequals(v,x,tc_set(tc_set(w))) ),
    inference(res,[status(thm),theory(equality)],[2,1]),
    [iquote('0:Res:2.0,1.0')] ).

cnf(113,plain,
    ( ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(u,v,w),v,tc_set(tc_set(w)))
    | ~ c_in(v,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
    | ~ c_in(c_Zorn_OTFin__linear__lemma1__1(u,v,w),c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
    | ~ c_in(x,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
    | ~ c_in(v,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
    | equal(c_Zorn_OTFin__linear__lemma1__1(u,v,w),v)
    | c_lessequals(x,v,tc_set(tc_set(w)))
    | c_lessequals(c_Zorn_Osucc(u,v,w),x,tc_set(tc_set(w))) ),
    inference(res,[status(thm),theory(equality)],[7,6]),
    [iquote('0:Res:7.4,6.2')] ).

cnf(115,plain,
    ( ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(u,v,w),v,tc_set(tc_set(w)))
    | ~ c_in(c_Zorn_OTFin__linear__lemma1__1(u,v,w),c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
    | ~ c_in(x,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
    | ~ c_in(v,c_Zorn_OTFin(u,w),tc_set(tc_set(w)))
    | equal(c_Zorn_OTFin__linear__lemma1__1(u,v,w),v)
    | c_lessequals(x,v,tc_set(tc_set(w)))
    | c_lessequals(c_Zorn_Osucc(u,v,w),x,tc_set(tc_set(w))) ),
    inference(obv,[status(thm),theory(equality)],[113]),
    [iquote('0:Obv:113.1')] ).

cnf(116,plain,
    ( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
    | ~ c_in(x,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
    | c_lessequals(u,x,tc_set(tc_set(w)))
    | c_lessequals(c_Zorn_Osucc(v,x,w),u,tc_set(tc_set(w))) ),
    inference(mrr,[status(thm)],[115,4,3,5]),
    [iquote('0:MRR:115.0,115.1,115.4,4.4,3.4,5.0')] ).

cnf(264,plain,
    ( ~ c_in(u,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
    | ~ c_in(x,c_Zorn_OTFin(v,w),tc_set(tc_set(w)))
    | c_lessequals(u,x,tc_set(tc_set(w)))
    | c_lessequals(x,u,tc_set(tc_set(w))) ),
    inference(res,[status(thm),theory(equality)],[116,42]),
    [iquote('0:Res:116.3,42.0')] ).

cnf(272,plain,
    ( ~ c_in(u,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | c_lessequals(v_m,u,tc_set(tc_set(t_a)))
    | c_lessequals(u,v_m,tc_set(tc_set(t_a))) ),
    inference(res,[status(thm),theory(equality)],[8,264]),
    [iquote('0:Res:8.0,264.0')] ).

cnf(274,plain,
    ( c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
    | c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
    inference(res,[status(thm),theory(equality)],[9,272]),
    [iquote('0:Res:9.0,272.0')] ).

cnf(277,plain,
    $false,
    inference(mrr,[status(thm)],[274,11,10]),
    [iquote('0:MRR:274.0,274.1,11.0,10.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SET858-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jul 11 00:59:27 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.49  
% 0.18/0.49  SPASS V 3.9 
% 0.18/0.49  SPASS beiseite: Proof found.
% 0.18/0.49  % SZS status Theorem
% 0.18/0.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.49  SPASS derived 253 clauses, backtracked 7 clauses, performed 2 splits and kept 155 clauses.
% 0.18/0.49  SPASS allocated 63807 KBytes.
% 0.18/0.49  SPASS spent	0:00:00.15 on the problem.
% 0.18/0.49  		0:00:00.04 for the input.
% 0.18/0.49  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.49  		0:00:00.01 for inferences.
% 0.18/0.49  		0:00:00.00 for the backtracking.
% 0.18/0.49  		0:00:00.07 for the reduction.
% 0.18/0.49  
% 0.18/0.49  
% 0.18/0.49  Here is a proof with depth 4, length 19 :
% 0.18/0.49  % SZS output start Refutation
% See solution above
% 0.18/0.49  Formulae used in the proof : cls_Set_Osubset__trans_0 cls_Zorn_OAbrial__axiom1_0 cls_Zorn_OTFin__linear__lemma1_0 cls_Zorn_OTFin__linear__lemma1_1 cls_Zorn_OTFin__linear__lemma1_2 cls_Zorn_OTFin__linear__lemma1_3 cls_Zorn_OTFin__linear__lemma2_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.18/0.49  
%------------------------------------------------------------------------------