TSTP Solution File: SET858-1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET858-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n004.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  : 300s
% DateTime : Fri May  3 03:01:50 EDT 2024

% Result   : Unsatisfiable 72.68s 10.67s
% Output   : CNFRefutation 72.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   33 (  10 unt;  15 nHn;  30 RR)
%            Number of literals    :  109 (  20 equ;  57 neg)
%            Maximal clause size   :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :   42 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c_49,plain,
    ( ~ c_lessequals(X0,X1,tc_set(X2))
    | ~ c_lessequals(X3,X0,tc_set(X2))
    | c_lessequals(X3,X1,tc_set(X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).

cnf(c_50,plain,
    c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).

cnf(c_51,plain,
    ( ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
    | ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
    | c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
    | c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
    | c_lessequals(X3,X0,tc_set(tc_set(X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).

cnf(c_52,plain,
    ( ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
    | ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
    | c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
    | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
    | c_lessequals(X3,X0,tc_set(tc_set(X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).

cnf(c_53,plain,
    ( c_Zorn_OTFin__linear__lemma1__1(X0,X1,X2) != X1
    | ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
    | ~ c_in(X3,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
    | c_lessequals(c_Zorn_Osucc(X0,X1,X2),X3,tc_set(tc_set(X2)))
    | c_lessequals(X3,X1,tc_set(tc_set(X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).

cnf(c_54,plain,
    ( ~ c_lessequals(c_Zorn_Osucc(X0,c_Zorn_OTFin__linear__lemma1__1(X0,X1,X2),X2),X1,tc_set(tc_set(X2)))
    | ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
    | ~ c_in(X3,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
    | c_lessequals(c_Zorn_Osucc(X0,X1,X2),X3,tc_set(tc_set(X2)))
    | c_lessequals(X3,X1,tc_set(tc_set(X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).

cnf(c_55,plain,
    ( ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
    | ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
    | ~ c_lessequals(X3,X0,tc_set(tc_set(X2)))
    | X0 = X3
    | c_lessequals(c_Zorn_Osucc(X1,X3,X2),X0,tc_set(tc_set(X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma2_0) ).

cnf(c_56,negated_conjecture,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(c_57,negated_conjecture,
    c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(c_58,negated_conjecture,
    ~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(c_59,negated_conjecture,
    ~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(c_1964,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_1966,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_2420,plain,
    ( ~ c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
    | ~ c_lessequals(v_n,X0,tc_set(tc_set(t_a)))
    | c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_3659,plain,
    ( c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a) != X0
    | ~ c_in(X0,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(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(v_m,X0,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_53]) ).

cnf(c_3663,plain,
    ( ~ c_in(X0,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(c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a),X0,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(v_m,X0,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_3667,plain,
    ( ~ c_in(X0,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_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(v_m,X0,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_3680,plain,
    ( ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a),t_a),X0,tc_set(tc_set(t_a)))
    | ~ c_in(X0,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(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(v_m,X0,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_6402,plain,
    ( ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_3667]) ).

cnf(c_6412,plain,
    ( c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) != v_n
    | ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_3659]) ).

cnf(c_6422,plain,
    ( ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a)))
    | c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_3663]) ).

cnf(c_6450,plain,
    ( ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a)))
    | ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_3680]) ).

cnf(c_6870,plain,
    ( X0 != X1
    | v_n != X1
    | X0 = v_n ),
    inference(instantiation,[status(thm)],[c_1966]) ).

cnf(c_9229,plain,
    ( ~ c_lessequals(c_Zorn_Osucc(X0,v_n,t_a),v_m,tc_set(tc_set(t_a)))
    | ~ c_lessequals(v_n,c_Zorn_Osucc(X0,v_n,t_a),tc_set(tc_set(t_a)))
    | c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_2420]) ).

cnf(c_9230,plain,
    c_lessequals(v_n,c_Zorn_Osucc(X0,v_n,t_a),tc_set(tc_set(t_a))),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_14399,plain,
    ( ~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
    | ~ c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a)))
    | c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_9229]) ).

cnf(c_17840,plain,
    c_lessequals(v_n,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a))),
    inference(instantiation,[status(thm)],[c_9230]) ).

cnf(c_21994,plain,
    ( ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),X0,tc_set(tc_set(t_a)))
    | ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | X0 = c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a)
    | c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),X0,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_28060,plain,
    ( c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) != X0
    | v_n != X0
    | c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) = v_n ),
    inference(instantiation,[status(thm)],[c_6870]) ).

cnf(c_29620,plain,
    ( c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) != c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a)
    | v_n != c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a)
    | c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) = v_n ),
    inference(instantiation,[status(thm)],[c_28060]) ).

cnf(c_29621,plain,
    c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) = c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),
    inference(instantiation,[status(thm)],[c_1964]) ).

cnf(c_31576,plain,
    ( ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a)))
    | ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | v_n = c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a)
    | c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a))) ),
    inference(instantiation,[status(thm)],[c_21994]) ).

cnf(c_31577,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_31576,c_29621,c_29620,c_17840,c_14399,c_6450,c_6422,c_6412,c_6402,c_56,c_57,c_58,c_59]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SET858-1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.10  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n004.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Thu May  2 20:14:18 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.16/0.41  Running first-order theorem proving
% 0.16/0.41  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 72.68/10.67  % SZS status Started for theBenchmark.p
% 72.68/10.67  % SZS status Unsatisfiable for theBenchmark.p
% 72.68/10.67  
% 72.68/10.67  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 72.68/10.67  
% 72.68/10.67  ------  iProver source info
% 72.68/10.67  
% 72.68/10.67  git: date: 2024-05-02 19:28:25 +0000
% 72.68/10.67  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 72.68/10.67  git: non_committed_changes: false
% 72.68/10.67  
% 72.68/10.67  ------ Parsing...successful
% 72.68/10.67  
% 72.68/10.67  
% 72.68/10.67  
% 72.68/10.67  ------ Preprocessing... sf_s  rm: 823 0s  sf_e  sf_s  rm: 43 0s  sf_e 
% 72.68/10.67  
% 72.68/10.67  ------ Preprocessing...
% 72.68/10.67  
% 72.68/10.67  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 72.68/10.67  ------ Proving...
% 72.68/10.67  ------ Problem Properties 
% 72.68/10.67  
% 72.68/10.67  
% 72.68/10.67  clauses                                 561
% 72.68/10.67  conjectures                             4
% 72.68/10.67  EPR                                     284
% 72.68/10.67  Horn                                    529
% 72.68/10.67  unary                                   129
% 72.68/10.67  binary                                  371
% 72.68/10.67  lits                                    1064
% 72.68/10.67  lits eq                                 159
% 72.68/10.67  fd_pure                                 0
% 72.68/10.67  fd_pseudo                               0
% 72.68/10.67  fd_cond                                 21
% 72.68/10.67  fd_pseudo_cond                          38
% 72.68/10.67  AC symbols                              0
% 72.68/10.67  
% 72.68/10.67  ------ Input Options Time Limit: Unbounded
% 72.68/10.67  
% 72.68/10.67  
% 72.68/10.67  ------ 
% 72.68/10.67  Current options:
% 72.68/10.67  ------ 
% 72.68/10.67  
% 72.68/10.67  
% 72.68/10.67  
% 72.68/10.67  
% 72.68/10.67  ------ Proving...
% 72.68/10.67  
% 72.68/10.67  
% 72.68/10.67  % SZS status Unsatisfiable for theBenchmark.p
% 72.68/10.67  
% 72.68/10.67  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 72.68/10.67  
% 72.68/10.67  
%------------------------------------------------------------------------------