TSTP Solution File: SET863-2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET863-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n023.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 : Thu Aug 31 14:36:03 EDT 2023

% Result   : Unsatisfiable 0.46s 0.59s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   65 (  15 unt;  17 typ;   0 def)
%            Number of atoms       :  125 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  140 (  63   ~;  77   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  10   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   7 con; 0-3 aty)
%            Number of variables   :   91 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    c_in: ( $i * $i * $i ) > $o ).

tff(decl_23,type,
    tc_set: $i > $i ).

tff(decl_24,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(decl_25,type,
    c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).

tff(decl_26,type,
    c_Zorn_Ochain: ( $i * $i ) > $i ).

tff(decl_27,type,
    c_Zorn_Ochain__extend__1: ( $i * $i * $i ) > $i ).

tff(decl_28,type,
    c_emptyset: $i ).

tff(decl_29,type,
    c_insert: ( $i * $i * $i ) > $i ).

tff(decl_30,type,
    c_union: ( $i * $i * $i ) > $i ).

tff(decl_31,type,
    c_Zorn_Omaxchain: ( $i * $i ) > $i ).

tff(decl_32,type,
    c_Zorn_Omaxchain__super__lemma__1: ( $i * $i * $i ) > $i ).

tff(decl_33,type,
    v_c: $i ).

tff(decl_34,type,
    v_S: $i ).

tff(decl_35,type,
    t_a: $i ).

tff(decl_36,type,
    v_x: $i ).

tff(decl_37,type,
    v_y: $i ).

tff(decl_38,type,
    v_xa: $i ).

cnf(cls_Zorn_Ochain__extend_0,axiom,
    ( c_in(c_Zorn_Ochain__extend__1(X4,X1,X3),X4,tc_set(X3))
    | c_in(c_union(c_insert(X1,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
    | ~ c_in(X1,X2,tc_set(X3))
    | ~ c_in(X4,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_Zorn_Omaxchain__super__lemma_1,axiom,
    ( c_in(X1,X6,X3)
    | ~ c_in(X1,X2,X3)
    | ~ c_in(X4,c_Zorn_Omaxchain(X5,X3),tc_set(tc_set(X3)))
    | ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X5,X3),tc_set(tc_set(X3)))
    | ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X4,X6,X3),X6,tc_set(X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_Zorn_Omaxchain__super__lemma_0,axiom,
    ( c_in(X1,X6,X3)
    | c_in(c_Zorn_Omaxchain__super__lemma__1(X4,X6,X3),X4,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | ~ c_in(X4,c_Zorn_Omaxchain(X5,X3),tc_set(tc_set(X3)))
    | ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X5,X3),tc_set(tc_set(X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).

cnf(cls_conjecture_7,negated_conjecture,
    ( c_lessequals(X1,v_y,tc_set(t_a))
    | ~ c_in(X1,v_c,tc_set(t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).

cnf(cls_Set_OsubsetD_0,axiom,
    ( c_in(X1,X4,X3)
    | ~ c_in(X1,X2,X3)
    | ~ c_lessequals(X2,X4,tc_set(X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

cnf(cls_conjecture_5,negated_conjecture,
    c_in(v_xa,v_x,t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

cnf(cls_conjecture_3,negated_conjecture,
    c_in(v_x,v_S,tc_set(t_a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_conjecture_6,negated_conjecture,
    ~ c_in(v_xa,v_y,t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

cnf(cls_conjecture_4,negated_conjecture,
    c_lessequals(v_y,v_x,tc_set(t_a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

cnf(cls_Set_OsubsetI_0,axiom,
    ( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
    | c_lessequals(X1,X2,tc_set(X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).

cnf(cls_Set_OsubsetI_1,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).

cnf(cls_Zorn_Ochain__extend_1,axiom,
    ( c_in(c_union(c_insert(X1,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
    | ~ c_in(X1,X2,tc_set(X3))
    | ~ c_in(X4,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
    | ~ c_lessequals(c_Zorn_Ochain__extend__1(X4,X1,X3),X1,tc_set(X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).

cnf(c_0_14,axiom,
    ( c_in(c_Zorn_Ochain__extend__1(X4,X1,X3),X4,tc_set(X3))
    | c_in(c_union(c_insert(X1,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
    | ~ c_in(X1,X2,tc_set(X3))
    | ~ c_in(X4,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3))) ),
    cls_Zorn_Ochain__extend_0 ).

cnf(c_0_15,negated_conjecture,
    c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
    cls_conjecture_1 ).

cnf(c_0_16,axiom,
    ( c_in(X1,X6,X3)
    | ~ c_in(X1,X2,X3)
    | ~ c_in(X4,c_Zorn_Omaxchain(X5,X3),tc_set(tc_set(X3)))
    | ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X5,X3),tc_set(tc_set(X3)))
    | ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X4,X6,X3),X6,tc_set(X3)) ),
    cls_Zorn_Omaxchain__super__lemma_1 ).

cnf(c_0_17,negated_conjecture,
    ( c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
    | c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
    | ~ c_in(X1,v_S,tc_set(t_a)) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
    cls_conjecture_0 ).

cnf(c_0_19,axiom,
    ( c_in(X1,X6,X3)
    | c_in(c_Zorn_Omaxchain__super__lemma__1(X4,X6,X3),X4,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | ~ c_in(X4,c_Zorn_Omaxchain(X5,X3),tc_set(tc_set(X3)))
    | ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X5,X3),tc_set(tc_set(X3))) ),
    cls_Zorn_Omaxchain__super__lemma_0 ).

cnf(c_0_20,negated_conjecture,
    ( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
    | c_in(X2,X3,t_a)
    | ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X3,t_a),X3,tc_set(t_a))
    | ~ c_in(X1,v_S,tc_set(t_a))
    | ~ c_in(X2,X1,t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).

cnf(c_0_21,negated_conjecture,
    ( c_lessequals(X1,v_y,tc_set(t_a))
    | ~ c_in(X1,v_c,tc_set(t_a)) ),
    cls_conjecture_7 ).

cnf(c_0_22,negated_conjecture,
    ( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
    | c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
    | c_in(X3,X2,t_a)
    | ~ c_in(X1,v_S,tc_set(t_a))
    | ~ c_in(X3,X1,t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_18])]) ).

cnf(c_0_23,axiom,
    ( c_in(X1,X4,X3)
    | ~ c_in(X1,X2,X3)
    | ~ c_lessequals(X2,X4,tc_set(X3)) ),
    cls_Set_OsubsetD_0 ).

cnf(c_0_24,negated_conjecture,
    ( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
    | c_in(X2,v_y,t_a)
    | ~ c_in(X1,v_S,tc_set(t_a))
    | ~ c_in(X2,X1,t_a) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).

cnf(c_0_25,negated_conjecture,
    c_in(v_xa,v_x,t_a),
    cls_conjecture_5 ).

cnf(c_0_26,negated_conjecture,
    c_in(v_x,v_S,tc_set(t_a)),
    cls_conjecture_3 ).

cnf(c_0_27,negated_conjecture,
    ~ c_in(v_xa,v_y,t_a),
    cls_conjecture_6 ).

cnf(c_0_28,negated_conjecture,
    ( c_in(X1,v_y,t_a)
    | ~ c_in(X2,v_c,tc_set(t_a))
    | ~ c_in(X1,X2,t_a) ),
    inference(spm,[status(thm)],[c_0_23,c_0_21]) ).

cnf(c_0_29,negated_conjecture,
    c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    c_lessequals(v_y,v_x,tc_set(t_a)),
    cls_conjecture_4 ).

cnf(c_0_31,negated_conjecture,
    ( c_in(X1,v_y,t_a)
    | ~ c_in(X1,c_Zorn_Ochain__extend__1(v_c,v_x,t_a),t_a) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_32,axiom,
    ( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
    | c_lessequals(X1,X2,tc_set(X3)) ),
    cls_Set_OsubsetI_0 ).

cnf(c_0_33,negated_conjecture,
    ( c_in(X1,v_x,t_a)
    | ~ c_in(X1,v_y,t_a) ),
    inference(spm,[status(thm)],[c_0_23,c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    ( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X1,tc_set(t_a))
    | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X1,t_a),v_y,t_a) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_35,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
    cls_Set_OsubsetI_1 ).

cnf(c_0_36,negated_conjecture,
    ( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X1,tc_set(t_a))
    | c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X1,t_a),v_x,t_a) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_37,axiom,
    ( c_in(c_union(c_insert(X1,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
    | ~ c_in(X1,X2,tc_set(X3))
    | ~ c_in(X4,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
    | ~ c_lessequals(c_Zorn_Ochain__extend__1(X4,X1,X3),X1,tc_set(X3)) ),
    cls_Zorn_Ochain__extend_1 ).

cnf(c_0_38,negated_conjecture,
    c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_39,negated_conjecture,
    ( c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(X1,t_a),tc_set(tc_set(t_a)))
    | ~ c_in(v_c,c_Zorn_Ochain(X1,t_a),tc_set(tc_set(t_a)))
    | ~ c_in(v_x,X1,tc_set(t_a)) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_40,negated_conjecture,
    ( c_in(X1,X2,t_a)
    | ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),X2,tc_set(t_a))
    | ~ c_in(v_c,c_Zorn_Omaxchain(X3,t_a),tc_set(tc_set(t_a)))
    | ~ c_in(v_c,c_Zorn_Ochain(X3,t_a),tc_set(tc_set(t_a)))
    | ~ c_in(v_x,X3,tc_set(t_a))
    | ~ c_in(X1,v_x,t_a) ),
    inference(spm,[status(thm)],[c_0_16,c_0_39]) ).

cnf(c_0_41,negated_conjecture,
    ( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
    | c_in(X2,X1,t_a)
    | ~ c_in(v_c,c_Zorn_Omaxchain(X3,t_a),tc_set(tc_set(t_a)))
    | ~ c_in(v_c,c_Zorn_Ochain(X3,t_a),tc_set(tc_set(t_a)))
    | ~ c_in(v_x,X3,tc_set(t_a))
    | ~ c_in(X2,v_x,t_a) ),
    inference(spm,[status(thm)],[c_0_19,c_0_39]) ).

cnf(c_0_42,negated_conjecture,
    ( c_in(X1,X2,t_a)
    | ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),X2,tc_set(t_a))
    | ~ c_in(X1,v_x,t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_18]),c_0_15]),c_0_26])]) ).

cnf(c_0_43,negated_conjecture,
    ( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
    | c_in(X2,X1,t_a)
    | ~ c_in(X2,v_x,t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_18]),c_0_15]),c_0_26])]) ).

cnf(c_0_44,negated_conjecture,
    ( c_in(X1,v_y,t_a)
    | ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a))
    | ~ c_in(X1,v_x,t_a) ),
    inference(spm,[status(thm)],[c_0_42,c_0_21]) ).

cnf(c_0_45,negated_conjecture,
    ( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
    | c_in(v_xa,X1,t_a) ),
    inference(spm,[status(thm)],[c_0_43,c_0_25]) ).

cnf(c_0_46,negated_conjecture,
    ( c_in(X1,v_y,t_a)
    | ~ c_in(X1,v_x,t_a) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_27]) ).

cnf(c_0_47,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_46]),c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SET863-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n023.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    : 300
% 0.13/0.34  % DateTime   : Sat Aug 26 16:13:56 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.46/0.57  start to proof: theBenchmark
% 0.46/0.59  % Version  : CSE_E---1.5
% 0.46/0.59  % Problem  : theBenchmark.p
% 0.46/0.59  % Proof found
% 0.46/0.59  % SZS status Theorem for theBenchmark.p
% 0.46/0.59  % SZS output start Proof
% See solution above
% 0.46/0.59  % Total time : 0.010000 s
% 0.46/0.59  % SZS output end Proof
% 0.46/0.59  % Total time : 0.013000 s
%------------------------------------------------------------------------------