TSTP Solution File: LAT276-2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT276-2 : 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 : 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  : 300s
% DateTime : Thu Aug 31 06:00:25 EDT 2023

% Result   : Unsatisfiable 0.19s 0.60s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   56 (   9 unt;  16 typ;   0 def)
%            Number of atoms       :   93 (   4 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  102 (  49   ~;  53   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (   9   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   7 con; 0-4 aty)
%            Number of variables   :   30 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    v_S: $i ).

tff(decl_23,type,
    v_A: $i ).

tff(decl_24,type,
    t_a: $i ).

tff(decl_25,type,
    tc_set: $i > $i ).

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

tff(decl_27,type,
    v_xa: $i ).

tff(decl_28,type,
    c_Pair: ( $i * $i * $i * $i ) > $i ).

tff(decl_29,type,
    v_cl: $i ).

tff(decl_30,type,
    tc_Product__Type_Ounit: $i ).

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

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

tff(decl_33,type,
    c_in: ( $i * $i * $i ) > $o ).

tff(decl_34,type,
    c_Tarski_Olub: ( $i * $i * $i ) > $i ).

tff(decl_35,type,
    c_Tarski_Opotype_Opset: ( $i * $i * $i ) > $i ).

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

tff(decl_37,type,
    v_sko__4mP: ( $i * $i * $i ) > $i ).

cnf(cls_conjecture_10,negated_conjecture,
    ( c_in(c_Pair(X1,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
    | ~ c_in(X1,v_S,t_a)
    | ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_10) ).

cnf(cls_Tarski_Or_A_61_61_Aorder_Acl_0,axiom,
    v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).

cnf(cls_conjecture_9,negated_conjecture,
    ( c_in(c_Pair(X1,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
    | c_in(v_xa,v_S,t_a)
    | ~ c_in(X1,v_S,t_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).

cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0,axiom,
    ( c_in(c_Pair(X1,c_Tarski_Olub(X2,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(X1,X2,t_a)
    | ~ c_lessequals(X2,v_A,tc_set(t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_lessequals(v_S,v_A,tc_set(t_a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_conjecture_4,negated_conjecture,
    ( c_in(v_xa,v_S,t_a)
    | ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
    ( c_in(c_Pair(c_Tarski_Olub(X2,v_cl,t_a),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(X1,v_A,t_a)
    | ~ c_in(c_Pair(v_sko__4mP(X1,X2,v_r),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_lessequals(X2,v_A,tc_set(t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1) ).

cnf(cls_conjecture_3,negated_conjecture,
    ( c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
    | c_in(v_xa,v_S,t_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_Tarski_OA_A_61_61_Apset_Acl_0,axiom,
    v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).

cnf(cls_conjecture_6,negated_conjecture,
    ( ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
    | ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
    ( c_in(c_Pair(c_Tarski_Olub(X2,v_cl,t_a),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | c_in(v_sko__4mP(X1,X2,v_r),X2,t_a)
    | ~ c_in(X1,v_A,t_a)
    | ~ c_lessequals(X2,v_A,tc_set(t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).

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(c_0_12,negated_conjecture,
    ( c_in(c_Pair(X1,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
    | ~ c_in(X1,v_S,t_a)
    | ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
    cls_conjecture_10 ).

cnf(c_0_13,axiom,
    v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
    cls_Tarski_Or_A_61_61_Aorder_Acl_0 ).

cnf(c_0_14,negated_conjecture,
    ( c_in(c_Pair(X1,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
    | c_in(v_xa,v_S,t_a)
    | ~ c_in(X1,v_S,t_a) ),
    cls_conjecture_9 ).

cnf(c_0_15,negated_conjecture,
    ( c_in(c_Pair(X1,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(X1,v_S,t_a) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).

cnf(c_0_16,axiom,
    ( c_in(c_Pair(X1,c_Tarski_Olub(X2,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(X1,X2,t_a)
    | ~ c_lessequals(X2,v_A,tc_set(t_a)) ),
    cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0 ).

cnf(c_0_17,negated_conjecture,
    c_lessequals(v_S,v_A,tc_set(t_a)),
    cls_conjecture_0 ).

cnf(c_0_18,negated_conjecture,
    ( c_in(c_Pair(X1,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | c_in(v_xa,v_S,t_a)
    | ~ c_in(X1,v_S,t_a) ),
    inference(rw,[status(thm)],[c_0_14,c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    ( c_in(v_xa,v_S,t_a)
    | ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
    cls_conjecture_4 ).

cnf(c_0_20,axiom,
    ( c_in(c_Pair(c_Tarski_Olub(X2,v_cl,t_a),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(X1,v_A,t_a)
    | ~ c_in(c_Pair(v_sko__4mP(X1,X2,v_r),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_lessequals(X2,v_A,tc_set(t_a)) ),
    cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1 ).

cnf(c_0_21,negated_conjecture,
    ( c_in(c_Pair(X1,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(X1,v_S,t_a) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    ( c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
    | c_in(v_xa,v_S,t_a) ),
    cls_conjecture_3 ).

cnf(c_0_23,axiom,
    v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
    cls_Tarski_OA_A_61_61_Apset_Acl_0 ).

cnf(c_0_24,negated_conjecture,
    ( ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
    | ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
    cls_conjecture_6 ).

cnf(c_0_25,axiom,
    ( c_in(c_Pair(c_Tarski_Olub(X2,v_cl,t_a),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | c_in(v_sko__4mP(X1,X2,v_r),X2,t_a)
    | ~ c_in(X1,v_A,t_a)
    | ~ c_lessequals(X2,v_A,tc_set(t_a)) ),
    cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0 ).

cnf(c_0_26,negated_conjecture,
    ( c_in(v_xa,v_S,t_a)
    | ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
    inference(rw,[status(thm)],[c_0_19,c_0_13]) ).

cnf(c_0_27,negated_conjecture,
    ( c_in(c_Pair(c_Tarski_Olub(X1,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(v_sko__4mP(v_xa,X1,v_r),v_S,t_a)
    | ~ c_in(v_xa,v_A,t_a)
    | ~ c_lessequals(X1,v_A,tc_set(t_a)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_28,negated_conjecture,
    ( c_in(v_xa,v_A,t_a)
    | c_in(v_xa,v_S,t_a) ),
    inference(rw,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_29,negated_conjecture,
    ( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_13]),c_0_13]) ).

cnf(c_0_30,negated_conjecture,
    ( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | c_in(v_sko__4mP(X1,v_S,v_r),v_S,t_a)
    | ~ c_in(X1,v_A,t_a) ),
    inference(spm,[status(thm)],[c_0_25,c_0_17]) ).

cnf(c_0_31,negated_conjecture,
    ( c_in(v_xa,v_S,t_a)
    | ~ c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_17])]),c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    ( c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)
    | ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(v_xa,v_A,t_a) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_33,negated_conjecture,
    c_in(v_xa,v_S,t_a),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_30]),c_0_28]),c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    ( c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)
    | ~ c_in(v_xa,v_A,t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_16]),c_0_17])]),c_0_33])]) ).

cnf(c_0_35,negated_conjecture,
    ( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(v_xa,v_A,t_a) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_17])]),c_0_34]) ).

cnf(c_0_36,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_37,negated_conjecture,
    ~ c_in(v_xa,v_A,t_a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_16]),c_0_33]),c_0_17])]) ).

cnf(c_0_38,negated_conjecture,
    ( c_in(X1,v_A,t_a)
    | ~ c_in(X1,v_S,t_a) ),
    inference(spm,[status(thm)],[c_0_36,c_0_17]) ).

cnf(c_0_39,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_33])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT276-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %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    : 300
% 0.12/0.33  % DateTime   : Thu Aug 24 07:02:22 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.60  % Version  : CSE_E---1.5
% 0.19/0.60  % Problem  : theBenchmark.p
% 0.19/0.60  % Proof found
% 0.19/0.60  % SZS status Theorem for theBenchmark.p
% 0.19/0.60  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.034000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.037000 s
%------------------------------------------------------------------------------