TSTP Solution File: GRP130-3.003 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP130-3.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n001.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 00:17:09 EDT 2023

% Result   : Unsatisfiable 0.19s 0.60s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   29
% Syntax   : Number of formulae    :  100 (  27 unt;  10 typ;   0 def)
%            Number of atoms       :  212 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  215 (  93   ~; 122   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   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    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   79 (   2 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,
    greater: ( $i * $i ) > $o ).

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

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

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

tff(decl_31,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)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).

cnf(element_1,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).

cnf(e_1_is_not_e_2,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

cnf(cycle7,axiom,
    ( equalish(X3,X4)
    | ~ cycle(X1,X2)
    | ~ product(X1,e_1,X3)
    | ~ greater(X2,e_0)
    | ~ next(X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cycle7) ).

cnf(cycle2,axiom,
    ( cycle(X1,e_0)
    | cycle(X1,e_1)
    | cycle(X1,e_2)
    | ~ group_element(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cycle2) ).

cnf(e_3_is_not_e_2,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

cnf(element_3,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).

cnf(e_1_greater_e_0,axiom,
    greater(e_1,e_0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_greater_e_0) ).

cnf(e_1_then_e_2,axiom,
    next(e_1,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_then_e_2) ).

cnf(qg3,negated_conjecture,
    ( product(X4,X2,X1)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).

cnf(product_total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).

cnf(e_3_is_not_e_1,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

cnf(product_left_cancellation,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).

cnf(product_right_cancellation,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).

cnf(element_2,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).

cnf(cycle6,axiom,
    ( ~ cycle(X1,e_0)
    | ~ product(X1,e_1,X2)
    | ~ greater(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cycle6) ).

cnf(e_2_is_not_e_1,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

cnf(e_3_greater_e_1,axiom,
    greater(e_3,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_1) ).

cnf(e_2_greater_e_0,axiom,
    greater(e_2,e_0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_greater_e_0) ).

cnf(c_0_19,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | product(X1,X2,e_3)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    product_total_function1 ).

cnf(c_0_20,axiom,
    group_element(e_1),
    element_1 ).

cnf(c_0_21,axiom,
    ~ equalish(e_1,e_2),
    e_1_is_not_e_2 ).

cnf(c_0_22,axiom,
    ( equalish(X3,X4)
    | ~ cycle(X1,X2)
    | ~ product(X1,e_1,X3)
    | ~ greater(X2,e_0)
    | ~ next(X1,X4) ),
    cycle7 ).

cnf(c_0_23,axiom,
    ( cycle(X1,e_0)
    | cycle(X1,e_1)
    | cycle(X1,e_2)
    | ~ group_element(X1) ),
    cycle2 ).

cnf(c_0_24,axiom,
    ~ equalish(e_3,e_2),
    e_3_is_not_e_2 ).

cnf(c_0_25,plain,
    ( product(X1,e_1,e_3)
    | product(X1,e_1,e_2)
    | product(X1,e_1,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_26,axiom,
    group_element(e_3),
    element_3 ).

cnf(c_0_27,plain,
    ( ~ product(X1,e_1,e_1)
    | ~ cycle(X1,X2)
    | ~ greater(X2,e_0)
    | ~ next(X1,e_2) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,plain,
    ( cycle(e_1,e_2)
    | cycle(e_1,e_1)
    | cycle(e_1,e_0) ),
    inference(spm,[status(thm)],[c_0_23,c_0_20]) ).

cnf(c_0_29,axiom,
    greater(e_1,e_0),
    e_1_greater_e_0 ).

cnf(c_0_30,axiom,
    next(e_1,e_2),
    e_1_then_e_2 ).

cnf(c_0_31,plain,
    ( ~ product(X1,e_1,e_3)
    | ~ cycle(X1,X2)
    | ~ greater(X2,e_0)
    | ~ next(X1,e_2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_22]) ).

cnf(c_0_32,negated_conjecture,
    ( product(X4,X2,X1)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X3,X4) ),
    qg3 ).

cnf(c_0_33,plain,
    ( product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_34,plain,
    ( cycle(e_1,e_0)
    | cycle(e_1,e_2)
    | ~ product(e_1,e_1,e_1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).

cnf(c_0_35,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2)
    | product(e_1,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_25,c_0_20]) ).

cnf(c_0_36,plain,
    ( cycle(e_1,e_0)
    | cycle(e_1,e_2)
    | ~ product(e_1,e_1,e_3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_28]),c_0_29]),c_0_30])]) ).

cnf(c_0_37,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    product_total_function2 ).

cnf(c_0_38,negated_conjecture,
    ( product(e_3,e_1,e_3)
    | product(e_3,e_1,e_2)
    | product(e_1,X1,e_3)
    | ~ product(e_3,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,axiom,
    ~ equalish(e_3,e_1),
    e_3_is_not_e_1 ).

cnf(c_0_40,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    product_left_cancellation ).

cnf(c_0_41,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    product_right_cancellation ).

cnf(c_0_42,plain,
    ( product(X1,e_3,e_3)
    | product(X1,e_3,e_2)
    | product(X1,e_3,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_26]) ).

cnf(c_0_43,axiom,
    group_element(e_2),
    element_2 ).

cnf(c_0_44,axiom,
    ( ~ cycle(X1,e_0)
    | ~ product(X1,e_1,X2)
    | ~ greater(X2,X1) ),
    cycle6 ).

cnf(c_0_45,plain,
    ( product(e_1,e_1,e_2)
    | cycle(e_1,e_2)
    | cycle(e_1,e_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_46,plain,
    ( ~ product(X1,X2,e_2)
    | ~ product(X1,X2,e_3) ),
    inference(spm,[status(thm)],[c_0_24,c_0_37]) ).

cnf(c_0_47,negated_conjecture,
    ( product(e_1,e_1,e_3)
    | product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_38,c_0_33]) ).

cnf(c_0_48,plain,
    ( ~ product(e_1,X1,X2)
    | ~ product(e_3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_49,axiom,
    ~ equalish(e_2,e_1),
    e_2_is_not_e_1 ).

cnf(c_0_50,plain,
    ( ~ product(X1,e_2,X2)
    | ~ product(X1,e_3,X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_41]) ).

cnf(c_0_51,plain,
    ( product(e_3,e_3,e_1)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_42,c_0_26]) ).

cnf(c_0_52,plain,
    ( product(X1,e_2,e_3)
    | product(X1,e_2,e_2)
    | product(X1,e_2,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_43]) ).

cnf(c_0_53,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_25,c_0_43]) ).

cnf(c_0_54,plain,
    ( product(e_1,e_1,e_2)
    | cycle(e_1,e_2)
    | ~ product(e_1,e_1,X1)
    | ~ greater(X1,e_1) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_55,axiom,
    greater(e_3,e_1),
    e_3_greater_e_1 ).

cnf(c_0_56,negated_conjecture,
    ( product(e_3,e_1,e_3)
    | ~ product(e_1,e_1,e_2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).

cnf(c_0_57,plain,
    ( ~ product(e_1,X1,X2)
    | ~ product(e_2,X1,X2) ),
    inference(spm,[status(thm)],[c_0_49,c_0_40]) ).

cnf(c_0_58,plain,
    ( ~ product(e_2,X1,X2)
    | ~ product(e_3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_40]) ).

cnf(c_0_59,plain,
    ( product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2)
    | ~ product(e_3,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_60,plain,
    ( product(e_3,e_2,e_1)
    | product(e_3,e_2,e_2)
    | product(e_3,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_52,c_0_26]) ).

cnf(c_0_61,negated_conjecture,
    ( product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2)
    | ~ product(e_3,X1,e_3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_51]),c_0_48]) ).

cnf(c_0_62,negated_conjecture,
    ( product(e_2,e_1,e_3)
    | product(e_2,e_1,e_2)
    | product(e_1,X1,e_2)
    | ~ product(e_2,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_53]) ).

cnf(c_0_63,negated_conjecture,
    ( product(e_3,e_1,e_3)
    | product(e_3,e_1,e_2)
    | cycle(e_1,e_2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_47]),c_0_55])]),c_0_56]) ).

cnf(c_0_64,axiom,
    greater(e_2,e_0),
    e_2_greater_e_0 ).

cnf(c_0_65,plain,
    ( ~ product(X1,e_1,X2)
    | ~ product(X1,e_3,X2) ),
    inference(spm,[status(thm)],[c_0_39,c_0_41]) ).

cnf(c_0_66,negated_conjecture,
    ( product(e_3,e_1,e_2)
    | ~ product(e_2,e_1,e_3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_47]),c_0_58]) ).

cnf(c_0_67,plain,
    ( product(e_3,e_2,e_2)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).

cnf(c_0_68,negated_conjecture,
    ( product(e_1,e_1,e_2)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_62,c_0_53]) ).

cnf(c_0_69,plain,
    ( ~ product(X1,e_1,X2)
    | ~ product(X1,e_2,X2) ),
    inference(spm,[status(thm)],[c_0_49,c_0_41]) ).

cnf(c_0_70,negated_conjecture,
    ( product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_63]),c_0_64]),c_0_30])]),c_0_47]) ).

cnf(c_0_71,negated_conjecture,
    ( ~ product(e_3,e_3,e_2)
    | ~ product(e_2,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_72,plain,
    ( product(e_3,e_3,e_2)
    | ~ product(e_3,e_2,e_3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_67]),c_0_46]) ).

cnf(c_0_73,negated_conjecture,
    ( product(e_2,e_1,e_3)
    | ~ product(e_3,e_1,e_2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_68]),c_0_58]) ).

cnf(c_0_74,negated_conjecture,
    ( product(e_3,e_1,e_2)
    | ~ product(e_3,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_75,negated_conjecture,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_3,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_76,plain,
    ( ~ product(X1,X2,e_1)
    | ~ product(X1,X2,e_3) ),
    inference(spm,[status(thm)],[c_0_39,c_0_37]) ).

cnf(c_0_77,negated_conjecture,
    ~ product(e_3,e_2,e_3),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).

cnf(c_0_78,negated_conjecture,
    ( product(e_3,e_1,e_2)
    | ~ product(e_3,X1,e_1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_70]),c_0_76]) ).

cnf(c_0_79,plain,
    ( product(e_3,e_2,e_2)
    | product(e_3,e_2,e_1) ),
    inference(sr,[status(thm)],[c_0_60,c_0_77]) ).

cnf(c_0_80,negated_conjecture,
    ( product(e_3,e_2,e_2)
    | product(e_3,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_81,negated_conjecture,
    ~ product(e_3,e_3,e_2),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_80]),c_0_50]) ).

cnf(c_0_82,negated_conjecture,
    ( product(e_3,e_2,e_3)
    | product(e_3,e_2,e_2)
    | product(e_1,X1,e_3)
    | ~ product(e_3,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_60]) ).

cnf(c_0_83,plain,
    ( product(e_3,e_3,e_3)
    | product(e_3,e_3,e_1) ),
    inference(sr,[status(thm)],[c_0_51,c_0_81]) ).

cnf(c_0_84,negated_conjecture,
    ( product(e_3,e_1,e_2)
    | ~ product(e_3,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_65,c_0_70]) ).

cnf(c_0_85,negated_conjecture,
    ( product(e_1,e_1,e_3)
    | product(e_3,e_2,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_80]),c_0_77]) ).

cnf(c_0_86,negated_conjecture,
    ( product(e_3,e_2,e_2)
    | product(e_2,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_73,c_0_80]) ).

cnf(c_0_87,negated_conjecture,
    product(e_3,e_1,e_2),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_83]),c_0_84]) ).

cnf(c_0_88,negated_conjecture,
    product(e_3,e_2,e_2),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_85]),c_0_86]) ).

cnf(c_0_89,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_87]),c_0_88])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP130-3.003 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n001.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 22:59:06 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  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 : 0.024000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.027000 s
%------------------------------------------------------------------------------