TSTP Solution File: GRP124-6.004 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP124-6.004 : 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 : n012.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 00:16:13 EDT 2023

% Result   : Unsatisfiable 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   85 (  28 unt;   8 typ;   0 def)
%            Number of atoms       :  178 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  161 (  60   ~; 101   |;   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  :    9 (   4   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   57 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    e_1: $i ).

tff(decl_23,type,
    group_element: $i > $o ).

tff(decl_24,type,
    e_2: $i ).

tff(decl_25,type,
    e_3: $i ).

tff(decl_26,type,
    e_4: $i ).

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

tff(decl_28,type,
    product1: ( $i * $i * $i ) > $o ).

tff(decl_29,type,
    product2: ( $i * $i * $i ) > $o ).

cnf(product1_total_function1,axiom,
    ( product1(X1,X2,e_1)
    | product1(X1,X2,e_2)
    | product1(X1,X2,e_3)
    | product1(X1,X2,e_4)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).

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

cnf(product1_right_cancellation,axiom,
    ( equalish(X2,X4)
    | ~ product1(X1,X2,X3)
    | ~ product1(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).

cnf(product1_idempotence,axiom,
    product1(X1,X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).

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

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

cnf(product1_left_cancellation,axiom,
    ( equalish(X1,X4)
    | ~ product1(X1,X2,X3)
    | ~ product1(X4,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_left_cancellation) ).

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_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_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(product2_total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product2(X1,X2,X3)
    | ~ product2(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).

cnf(product2_idempotence,axiom,
    product2(X1,X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).

cnf(qg2a,negated_conjecture,
    ( product2(X4,X2,X1)
    | ~ product1(X1,X2,X3)
    | ~ product1(X3,X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2a) ).

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(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_1_is_not_e_3,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).

cnf(c_0_16,axiom,
    ( product1(X1,X2,e_1)
    | product1(X1,X2,e_2)
    | product1(X1,X2,e_3)
    | product1(X1,X2,e_4)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    product1_total_function1 ).

cnf(c_0_17,axiom,
    group_element(e_4),
    element_4 ).

cnf(c_0_18,axiom,
    ( equalish(X2,X4)
    | ~ product1(X1,X2,X3)
    | ~ product1(X1,X4,X3) ),
    product1_right_cancellation ).

cnf(c_0_19,axiom,
    product1(X1,X1,X1),
    product1_idempotence ).

cnf(c_0_20,plain,
    ( product1(X1,e_4,e_4)
    | product1(X1,e_4,e_3)
    | product1(X1,e_4,e_2)
    | product1(X1,e_4,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,axiom,
    group_element(e_1),
    element_1 ).

cnf(c_0_22,axiom,
    group_element(e_3),
    element_3 ).

cnf(c_0_23,axiom,
    ( equalish(X1,X4)
    | ~ product1(X1,X2,X3)
    | ~ product1(X4,X2,X3) ),
    product1_left_cancellation ).

cnf(c_0_24,plain,
    ( equalish(X1,X2)
    | ~ product1(X2,X1,X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_25,plain,
    ( product1(e_1,e_4,e_1)
    | product1(e_1,e_4,e_2)
    | product1(e_1,e_4,e_3)
    | product1(e_1,e_4,e_4) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,axiom,
    ~ equalish(e_4,e_1),
    e_4_is_not_e_1 ).

cnf(c_0_27,plain,
    ( product1(X1,e_3,e_4)
    | product1(X1,e_3,e_3)
    | product1(X1,e_3,e_2)
    | product1(X1,e_3,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_22]) ).

cnf(c_0_28,plain,
    ( equalish(X1,X2)
    | ~ product1(X1,X2,X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_19]) ).

cnf(c_0_29,plain,
    ( product1(e_1,e_4,e_4)
    | product1(e_1,e_4,e_3)
    | product1(e_1,e_4,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

cnf(c_0_30,axiom,
    ~ equalish(e_1,e_4),
    e_1_is_not_e_4 ).

cnf(c_0_31,plain,
    ( product1(e_1,e_3,e_1)
    | product1(e_1,e_3,e_2)
    | product1(e_1,e_3,e_3)
    | product1(e_1,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_27,c_0_21]) ).

cnf(c_0_32,axiom,
    ~ equalish(e_3,e_1),
    e_3_is_not_e_1 ).

cnf(c_0_33,plain,
    ( product1(X1,e_1,e_4)
    | product1(X1,e_1,e_3)
    | product1(X1,e_1,e_2)
    | product1(X1,e_1,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_21]) ).

cnf(c_0_34,axiom,
    ( equalish(X3,X4)
    | ~ product2(X1,X2,X3)
    | ~ product2(X1,X2,X4) ),
    product2_total_function2 ).

cnf(c_0_35,axiom,
    product2(X1,X1,X1),
    product2_idempotence ).

cnf(c_0_36,negated_conjecture,
    ( product2(X4,X2,X1)
    | ~ product1(X1,X2,X3)
    | ~ product1(X3,X1,X4) ),
    qg2a ).

cnf(c_0_37,plain,
    ( product1(e_1,e_4,e_2)
    | product1(e_1,e_4,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).

cnf(c_0_38,plain,
    ( product1(e_1,e_3,e_4)
    | product1(e_1,e_3,e_3)
    | product1(e_1,e_3,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_31]),c_0_32]) ).

cnf(c_0_39,plain,
    ( product1(e_4,e_1,e_1)
    | product1(e_4,e_1,e_2)
    | product1(e_4,e_1,e_3)
    | product1(e_4,e_1,e_4) ),
    inference(spm,[status(thm)],[c_0_33,c_0_17]) ).

cnf(c_0_40,plain,
    ( equalish(X1,X2)
    | ~ product2(X2,X2,X1) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_41,negated_conjecture,
    ( product2(e_3,X1,e_4)
    | product1(e_1,e_4,e_2)
    | ~ product1(e_4,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_42,axiom,
    ~ equalish(e_4,e_3),
    e_4_is_not_e_3 ).

cnf(c_0_43,negated_conjecture,
    ( product2(e_4,X1,e_3)
    | product1(e_1,e_3,e_2)
    | product1(e_1,e_3,e_3)
    | ~ product1(e_3,X1,e_1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_38]) ).

cnf(c_0_44,axiom,
    ~ equalish(e_3,e_4),
    e_3_is_not_e_4 ).

cnf(c_0_45,plain,
    ( product1(e_4,e_1,e_4)
    | product1(e_4,e_1,e_3)
    | product1(e_4,e_1,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_39]),c_0_26]) ).

cnf(c_0_46,negated_conjecture,
    ( product1(e_1,e_4,e_2)
    | ~ product1(e_4,e_3,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).

cnf(c_0_47,negated_conjecture,
    ( product1(e_1,e_3,e_3)
    | product1(e_1,e_3,e_2)
    | ~ product1(e_3,e_4,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_43]),c_0_44]) ).

cnf(c_0_48,axiom,
    ~ equalish(e_1,e_3),
    e_1_is_not_e_3 ).

cnf(c_0_49,plain,
    ( product1(e_4,e_1,e_2)
    | product1(e_4,e_1,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_45]),c_0_30]) ).

cnf(c_0_50,negated_conjecture,
    ( equalish(X1,e_4)
    | ~ product1(e_4,e_3,e_1)
    | ~ product1(e_1,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_46]) ).

cnf(c_0_51,negated_conjecture,
    ( product1(e_1,e_3,e_2)
    | ~ product1(e_3,e_4,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_47]),c_0_48]) ).

cnf(c_0_52,negated_conjecture,
    ( product2(e_3,X1,e_1)
    | product1(e_4,e_1,e_2)
    | ~ product1(e_1,X1,e_4) ),
    inference(spm,[status(thm)],[c_0_36,c_0_49]) ).

cnf(c_0_53,negated_conjecture,
    ( ~ product1(e_4,e_3,e_1)
    | ~ product1(e_3,e_4,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_44]) ).

cnf(c_0_54,plain,
    ( product1(e_4,e_3,e_1)
    | product1(e_4,e_3,e_2)
    | product1(e_4,e_3,e_3)
    | product1(e_4,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_27,c_0_17]) ).

cnf(c_0_55,negated_conjecture,
    ( product1(e_4,e_1,e_2)
    | ~ product1(e_1,e_3,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_52]),c_0_48]) ).

cnf(c_0_56,negated_conjecture,
    ( product1(e_4,e_3,e_4)
    | product1(e_4,e_3,e_3)
    | product1(e_4,e_3,e_2)
    | ~ product1(e_3,e_4,e_1) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_57,negated_conjecture,
    ( product1(e_1,e_3,e_2)
    | product1(e_1,e_3,e_3)
    | product1(e_4,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_55,c_0_38]) ).

cnf(c_0_58,negated_conjecture,
    ( product1(e_4,e_3,e_2)
    | product1(e_4,e_3,e_3)
    | ~ product1(e_3,e_4,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_56]),c_0_44]) ).

cnf(c_0_59,negated_conjecture,
    ( product1(e_4,e_1,e_2)
    | product1(e_1,e_3,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_57]),c_0_48]) ).

cnf(c_0_60,negated_conjecture,
    ( product1(e_4,e_3,e_2)
    | ~ product1(e_3,e_4,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_58]),c_0_42]) ).

cnf(c_0_61,negated_conjecture,
    ( product1(e_4,e_1,e_2)
    | equalish(X1,e_1)
    | ~ product1(X1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_59]) ).

cnf(c_0_62,negated_conjecture,
    ( equalish(X1,e_3)
    | ~ product1(e_3,e_4,e_1)
    | ~ product1(e_4,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_60]) ).

cnf(c_0_63,negated_conjecture,
    ( product1(e_4,e_1,e_2)
    | ~ product1(e_3,e_4,e_1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_60]),c_0_26]) ).

cnf(c_0_64,plain,
    ( product1(e_3,e_4,e_1)
    | product1(e_3,e_4,e_2)
    | product1(e_3,e_4,e_3)
    | product1(e_3,e_4,e_4) ),
    inference(spm,[status(thm)],[c_0_20,c_0_22]) ).

cnf(c_0_65,negated_conjecture,
    ~ product1(e_3,e_4,e_1),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_48]) ).

cnf(c_0_66,plain,
    ( product1(e_3,e_4,e_4)
    | product1(e_3,e_4,e_3)
    | product1(e_3,e_4,e_2) ),
    inference(sr,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_67,plain,
    ( product1(e_3,e_4,e_2)
    | product1(e_3,e_4,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_66]),c_0_44]) ).

cnf(c_0_68,plain,
    product1(e_3,e_4,e_2),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_67]),c_0_42]) ).

cnf(c_0_69,plain,
    ( equalish(X1,e_3)
    | ~ product1(X1,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_68]) ).

cnf(c_0_70,negated_conjecture,
    ~ product1(e_4,e_3,e_1),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_46]),c_0_48]) ).

cnf(c_0_71,plain,
    ( product1(e_4,e_3,e_4)
    | product1(e_4,e_3,e_3)
    | product1(e_4,e_3,e_2) ),
    inference(sr,[status(thm)],[c_0_54,c_0_70]) ).

cnf(c_0_72,plain,
    ( product1(e_4,e_3,e_2)
    | product1(e_4,e_3,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_71]),c_0_44]) ).

cnf(c_0_73,plain,
    product1(e_4,e_3,e_2),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_72]),c_0_42]) ).

cnf(c_0_74,plain,
    ( equalish(X1,e_3)
    | ~ product1(e_4,X1,e_2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_73]) ).

cnf(c_0_75,negated_conjecture,
    product1(e_4,e_1,e_2),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_73]),c_0_26]) ).

cnf(c_0_76,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_48]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP124-6.004 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n012.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 21:30:39 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.029000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.032000 s
%------------------------------------------------------------------------------