TSTP Solution File: GRP126-3.004 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP126-3.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n020.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 00:16:28 EDT 2023

% Result   : Unsatisfiable 0.19s 0.62s
% Output   : CNFRefutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   90 (  28 unt;  11 typ;   0 def)
%            Number of atoms       :  198 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  172 (  53   ~; 119   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   56 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    e_0: $i ).

tff(decl_23,type,
    e_1: $i ).

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

tff(decl_25,type,
    e_2: $i ).

tff(decl_26,type,
    e_3: $i ).

tff(decl_27,type,
    e_4: $i ).

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

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

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

tff(decl_31,type,
    group_element: $i > $o ).

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

cnf(product_total_function1,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | product(X1,X2,e_3)
    | product(X1,X2,e_4)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).

cnf(element_4,axiom,
    group_element(e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).

cnf(product_left_cancellation,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).

cnf(product_idempotence,axiom,
    product(X1,X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).

cnf(element_3,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).

cnf(product_right_cancellation,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).

cnf(e_3_is_not_e_4,axiom,
    ~ equalish(e_3,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).

cnf(e_4_is_not_e_3,axiom,
    ~ equalish(e_4,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).

cnf(qg4,negated_conjecture,
    ( product(X3,X4,X2)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4) ).

cnf(element_2,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).

cnf(e_2_is_not_e_4,axiom,
    ~ equalish(e_2,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).

cnf(product_total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).

cnf(e_3_is_not_e_2,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

cnf(e_1_is_not_e_4,axiom,
    ~ equalish(e_1,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).

cnf(e_4_is_not_e_2,axiom,
    ~ equalish(e_4,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).

cnf(e_2_is_not_e_3,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

cnf(e_4_is_not_e_1,axiom,
    ~ equalish(e_4,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).

cnf(e_3_is_not_e_1,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

cnf(c_0_18,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | product(X1,X2,e_3)
    | product(X1,X2,e_4)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    product_total_function1 ).

cnf(c_0_19,axiom,
    group_element(e_4),
    element_4 ).

cnf(c_0_20,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    product_left_cancellation ).

cnf(c_0_21,axiom,
    product(X1,X1,X1),
    product_idempotence ).

cnf(c_0_22,plain,
    ( product(X1,e_4,e_1)
    | product(X1,e_4,e_2)
    | product(X1,e_4,e_3)
    | product(X1,e_4,e_4)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,axiom,
    group_element(e_3),
    element_3 ).

cnf(c_0_24,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    product_right_cancellation ).

cnf(c_0_25,plain,
    ( equalish(X1,X2)
    | ~ product(X1,X2,X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,plain,
    ( product(e_3,e_4,e_1)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_3)
    | product(e_3,e_4,e_4) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_27,axiom,
    ~ equalish(e_3,e_4),
    e_3_is_not_e_4 ).

cnf(c_0_28,plain,
    ( product(X1,e_3,e_1)
    | product(X1,e_3,e_2)
    | product(X1,e_3,e_3)
    | product(X1,e_3,e_4)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_23]) ).

cnf(c_0_29,plain,
    ( equalish(X1,X2)
    | ~ product(X2,X1,X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_21]) ).

cnf(c_0_30,plain,
    ( product(e_3,e_4,e_1)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

cnf(c_0_31,axiom,
    ~ equalish(e_4,e_3),
    e_4_is_not_e_3 ).

cnf(c_0_32,plain,
    ( product(e_4,e_3,e_1)
    | product(e_4,e_3,e_2)
    | product(e_4,e_3,e_3)
    | product(e_4,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_28,c_0_19]) ).

cnf(c_0_33,negated_conjecture,
    ( product(X3,X4,X2)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X1,X4) ),
    qg4 ).

cnf(c_0_34,plain,
    ( product(e_3,e_4,e_1)
    | product(e_3,e_4,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).

cnf(c_0_35,plain,
    ( product(e_4,e_3,e_1)
    | product(e_4,e_3,e_2)
    | product(e_4,e_3,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_27]) ).

cnf(c_0_36,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(X1,e_2,e_3)
    | ~ product(e_4,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_37,plain,
    ( product(e_4,e_3,e_1)
    | product(e_4,e_3,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_35]),c_0_31]) ).

cnf(c_0_38,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_2,e_2,e_3)
    | product(e_4,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_39,negated_conjecture,
    ( product(e_3,e_4,e_1)
    | product(e_1,e_2,e_3)
    | product(e_2,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_36,c_0_38]) ).

cnf(c_0_40,axiom,
    group_element(e_2),
    element_2 ).

cnf(c_0_41,negated_conjecture,
    ( product(e_1,e_2,e_3)
    | product(e_2,e_2,e_3)
    | product(X1,e_1,e_3)
    | ~ product(e_4,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_39]) ).

cnf(c_0_42,plain,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2)
    | product(e_2,e_4,e_3)
    | product(e_2,e_4,e_4) ),
    inference(spm,[status(thm)],[c_0_22,c_0_40]) ).

cnf(c_0_43,axiom,
    ~ equalish(e_2,e_4),
    e_2_is_not_e_4 ).

cnf(c_0_44,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    product_total_function2 ).

cnf(c_0_45,negated_conjecture,
    ( product(e_1,e_2,e_3)
    | product(e_2,e_2,e_3)
    | product(e_2,e_1,e_3)
    | product(e_4,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_41,c_0_37]) ).

cnf(c_0_46,plain,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2)
    | product(e_2,e_4,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_42]),c_0_43]) ).

cnf(c_0_47,plain,
    ( equalish(X1,X2)
    | ~ product(X2,X2,X1) ),
    inference(spm,[status(thm)],[c_0_44,c_0_21]) ).

cnf(c_0_48,negated_conjecture,
    ( product(e_1,e_2,e_3)
    | product(e_2,e_2,e_3)
    | product(e_1,e_1,e_3)
    | product(e_2,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_41,c_0_45]) ).

cnf(c_0_49,axiom,
    ~ equalish(e_3,e_2),
    e_3_is_not_e_2 ).

cnf(c_0_50,plain,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2)
    | equalish(X1,e_4)
    | ~ product(e_2,X1,e_3) ),
    inference(spm,[status(thm)],[c_0_24,c_0_46]) ).

cnf(c_0_51,negated_conjecture,
    ( product(e_1,e_2,e_3)
    | product(e_1,e_1,e_3)
    | product(e_2,e_1,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).

cnf(c_0_52,axiom,
    ~ equalish(e_1,e_4),
    e_1_is_not_e_4 ).

cnf(c_0_53,plain,
    ( product(X1,e_2,e_1)
    | product(X1,e_2,e_2)
    | product(X1,e_2,e_3)
    | product(X1,e_2,e_4)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_40]) ).

cnf(c_0_54,negated_conjecture,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2)
    | product(e_1,e_2,e_3)
    | product(e_1,e_1,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).

cnf(c_0_55,axiom,
    ~ equalish(e_4,e_2),
    e_4_is_not_e_2 ).

cnf(c_0_56,plain,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | product(e_4,e_2,e_3)
    | product(e_4,e_2,e_4) ),
    inference(spm,[status(thm)],[c_0_53,c_0_19]) ).

cnf(c_0_57,negated_conjecture,
    ( product(e_1,e_2,e_3)
    | product(e_2,e_2,e_3)
    | equalish(X1,e_3)
    | ~ product(X1,e_4,e_1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_39]) ).

cnf(c_0_58,negated_conjecture,
    ( product(e_2,e_4,e_1)
    | product(e_1,e_2,e_3)
    | product(e_1,e_1,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_54]),c_0_55]) ).

cnf(c_0_59,axiom,
    ~ equalish(e_2,e_3),
    e_2_is_not_e_3 ).

cnf(c_0_60,plain,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | product(e_4,e_2,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_56]),c_0_43]) ).

cnf(c_0_61,negated_conjecture,
    ( product(e_1,e_2,e_3)
    | product(e_2,e_2,e_3)
    | product(e_1,e_1,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).

cnf(c_0_62,plain,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | equalish(X1,e_4)
    | ~ product(X1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_20,c_0_60]) ).

cnf(c_0_63,negated_conjecture,
    ( product(e_1,e_2,e_3)
    | product(e_1,e_1,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_61]),c_0_49]) ).

cnf(c_0_64,negated_conjecture,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | product(e_1,e_1,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_52]) ).

cnf(c_0_65,negated_conjecture,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2)
    | product(X1,e_3,e_2)
    | ~ product(e_4,e_2,X1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_46]) ).

cnf(c_0_66,negated_conjecture,
    ( product(e_4,e_2,e_1)
    | product(e_1,e_1,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_64]),c_0_55]) ).

cnf(c_0_67,negated_conjecture,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2)
    | product(e_1,e_3,e_2)
    | product(e_1,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_68,negated_conjecture,
    ( product(e_1,e_1,e_3)
    | product(X1,e_1,e_4)
    | ~ product(e_2,e_4,X1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_66]) ).

cnf(c_0_69,negated_conjecture,
    ( product(e_2,e_4,e_1)
    | product(e_1,e_3,e_2)
    | product(e_1,e_1,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_67]),c_0_55]) ).

cnf(c_0_70,plain,
    ( product(e_4,e_3,e_1)
    | equalish(X1,e_4)
    | ~ product(X1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_37]) ).

cnf(c_0_71,negated_conjecture,
    ( product(e_1,e_1,e_3)
    | product(e_1,e_1,e_4)
    | product(e_1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_72,negated_conjecture,
    ( product(e_1,e_1,e_3)
    | equalish(X1,e_2)
    | ~ product(e_4,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_66]) ).

cnf(c_0_73,negated_conjecture,
    ( product(e_4,e_3,e_1)
    | product(e_1,e_1,e_3)
    | product(e_1,e_1,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_52]) ).

cnf(c_0_74,negated_conjecture,
    ( product(e_1,e_1,e_3)
    | product(e_1,e_1,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_49]) ).

cnf(c_0_75,axiom,
    ~ equalish(e_4,e_1),
    e_4_is_not_e_1 ).

cnf(c_0_76,negated_conjecture,
    product(e_1,e_1,e_3),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_74]),c_0_75]) ).

cnf(c_0_77,axiom,
    ~ equalish(e_3,e_1),
    e_3_is_not_e_1 ).

cnf(c_0_78,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_76]),c_0_77]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem    : GRP126-3.004 : TPTP v8.1.2. Released v1.2.0.
% 0.08/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n020.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   : Mon Aug 28 21:27:13 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 0.19/0.62  % Version  : CSE_E---1.5
% 0.19/0.62  % Problem  : theBenchmark.p
% 0.19/0.62  % Proof found
% 0.19/0.62  % SZS status Theorem for theBenchmark.p
% 0.19/0.62  % SZS output start Proof
% See solution above
% 0.56/0.62  % Total time : 0.033000 s
% 0.56/0.62  % SZS output end Proof
% 0.56/0.62  % Total time : 0.036000 s
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