TSTP Solution File: GRP025-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP025-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n025.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 00:13:40 EDT 2023

% Result   : Unsatisfiable 0.18s 0.57s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   88 (  35 unt;  15 typ;   0 def)
%            Number of atoms       :  130 (  74 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   98 (  41   ~;  57   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (   6   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-4 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-3 aty)
%            Number of variables   :   24 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

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

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

tff(decl_28,type,
    g1: $i ).

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

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

tff(decl_31,type,
    g2: $i ).

tff(decl_32,type,
    d: $i ).

tff(decl_33,type,
    an_isomorphism: $i > $i ).

tff(decl_34,type,
    d1: $i ).

tff(decl_35,type,
    d2: $i ).

tff(decl_36,type,
    d3: $i ).

cnf(a_and_b_only_members_of_group1,hypothesis,
    ( X1 = a
    | X1 = b
    | ~ group_member(X1,g1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_and_b_only_members_of_group1) ).

cnf(d3_member_of_group1,hypothesis,
    group_member(d3,g1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_member_of_group1) ).

cnf(d2_member_of_group1,hypothesis,
    group_member(d2,g1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_member_of_group1) ).

cnf(prove_product_holds_in_group2,negated_conjecture,
    ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_holds_in_group2) ).

cnf(b_maps_to_d,hypothesis,
    an_isomorphism(b) = d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_maps_to_d) ).

cnf(d1_member_of_group1,hypothesis,
    group_member(d1,g1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_member_of_group1) ).

cnf(a_maps_to_c,hypothesis,
    an_isomorphism(a) = c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_maps_to_c) ).

cnf(c_times_d_is_d,hypothesis,
    product(g2,c,d,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_d_is_d) ).

cnf(d1_times_d2_is_d3,hypothesis,
    product(g1,d1,d2,d3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_times_d2_is_d3) ).

cnf(total_function2,axiom,
    ( X5 = X4
    | ~ product(X1,X2,X3,X4)
    | ~ product(X1,X2,X3,X5) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',total_function2) ).

cnf(c_times_c_is_c,hypothesis,
    product(g2,c,c,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_c_is_c) ).

cnf(b_times_b_is_a,hypothesis,
    product(g1,b,b,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_b_is_a) ).

cnf(d_times_d_is_c,hypothesis,
    product(g2,d,d,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_d_is_c) ).

cnf(a_times_a_is_a,hypothesis,
    product(g1,a,a,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_a_is_a) ).

cnf(a_times_b_is_b,hypothesis,
    product(g1,a,b,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_b) ).

cnf(b_times_a_is_b,hypothesis,
    product(g1,b,a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_is_b) ).

cnf(d_times_c_is_d,hypothesis,
    product(g2,d,c,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_c_is_d) ).

cnf(c_0_17,hypothesis,
    ( X1 = a
    | X1 = b
    | ~ group_member(X1,g1) ),
    a_and_b_only_members_of_group1 ).

cnf(c_0_18,hypothesis,
    group_member(d3,g1),
    d3_member_of_group1 ).

cnf(c_0_19,hypothesis,
    ( d3 = b
    | d3 = a ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_20,hypothesis,
    group_member(d2,g1),
    d2_member_of_group1 ).

cnf(c_0_21,negated_conjecture,
    ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
    prove_product_holds_in_group2 ).

cnf(c_0_22,hypothesis,
    ( d3 = b
    | a != b ),
    inference(ef,[status(thm)],[c_0_19]) ).

cnf(c_0_23,hypothesis,
    an_isomorphism(b) = d,
    b_maps_to_d ).

cnf(c_0_24,hypothesis,
    ( d2 = b
    | d2 = a ),
    inference(spm,[status(thm)],[c_0_17,c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    ( a != b
    | ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),d) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_26,hypothesis,
    ( d2 = b
    | a != b ),
    inference(ef,[status(thm)],[c_0_24]) ).

cnf(c_0_27,hypothesis,
    group_member(d1,g1),
    d1_member_of_group1 ).

cnf(c_0_28,hypothesis,
    ( a != b
    | ~ product(g2,an_isomorphism(d1),d,d) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).

cnf(c_0_29,hypothesis,
    ( d1 = b
    | d1 = a ),
    inference(spm,[status(thm)],[c_0_17,c_0_27]) ).

cnf(c_0_30,hypothesis,
    an_isomorphism(a) = c,
    a_maps_to_c ).

cnf(c_0_31,hypothesis,
    product(g2,c,d,d),
    c_times_d_is_d ).

cnf(c_0_32,hypothesis,
    product(g1,d1,d2,d3),
    d1_times_d2_is_d3 ).

cnf(c_0_33,hypothesis,
    ( d1 = b
    | a != b ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).

cnf(c_0_34,negated_conjecture,
    ( d3 = b
    | ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),c) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_30]) ).

cnf(c_0_35,axiom,
    ( X5 = X4
    | ~ product(X1,X2,X3,X4)
    | ~ product(X1,X2,X3,X5) ),
    total_function2 ).

cnf(c_0_36,hypothesis,
    ( product(g1,b,d2,d3)
    | a != b ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_37,hypothesis,
    ( d2 = b
    | d3 = b
    | ~ product(g2,an_isomorphism(d1),c,c) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_24]),c_0_30]) ).

cnf(c_0_38,hypothesis,
    product(g2,c,c,c),
    c_times_c_is_c ).

cnf(c_0_39,hypothesis,
    ( X1 = d3
    | a != b
    | ~ product(g1,b,d2,X1) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_40,hypothesis,
    ( d1 = b
    | d3 = b
    | d2 = b ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_29]),c_0_30]),c_0_38])]) ).

cnf(c_0_41,negated_conjecture,
    ( a != b
    | ~ product(g2,an_isomorphism(d1),d,an_isomorphism(d3)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_26]),c_0_23]) ).

cnf(c_0_42,hypothesis,
    ( X1 = d3
    | a != b
    | ~ product(g1,b,b,X1) ),
    inference(spm,[status(thm)],[c_0_39,c_0_26]) ).

cnf(c_0_43,hypothesis,
    product(g1,b,b,a),
    b_times_b_is_a ).

cnf(c_0_44,hypothesis,
    ( d2 = b
    | d1 = b
    | product(g1,d1,d2,b) ),
    inference(spm,[status(thm)],[c_0_32,c_0_40]) ).

cnf(c_0_45,hypothesis,
    ( a != b
    | ~ product(g2,d,d,an_isomorphism(d3)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_33]),c_0_23]) ).

cnf(c_0_46,hypothesis,
    ( d3 = a
    | a != b ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_47,hypothesis,
    product(g2,d,d,c),
    d_times_d_is_c ).

cnf(c_0_48,hypothesis,
    ( d1 = b
    | d2 = b
    | X1 = b
    | ~ product(g1,d1,d2,X1) ),
    inference(spm,[status(thm)],[c_0_35,c_0_44]) ).

cnf(c_0_49,hypothesis,
    a != b,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_30]),c_0_47])]) ).

cnf(c_0_50,hypothesis,
    ( d2 = b
    | d1 = b
    | X1 = b
    | ~ product(g1,d1,a,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_24]),c_0_49]) ).

cnf(c_0_51,hypothesis,
    ( X1 = d3
    | ~ product(g1,d1,d2,X1) ),
    inference(spm,[status(thm)],[c_0_35,c_0_32]) ).

cnf(c_0_52,hypothesis,
    ( d1 = b
    | d2 = b
    | X1 = b
    | ~ product(g1,a,a,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_29]),c_0_49]) ).

cnf(c_0_53,hypothesis,
    product(g1,a,a,a),
    a_times_a_is_a ).

cnf(c_0_54,hypothesis,
    ( d1 = b
    | X1 = d3
    | ~ product(g1,a,d2,X1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_29]) ).

cnf(c_0_55,hypothesis,
    ( d2 = b
    | d1 = b ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_49]) ).

cnf(c_0_56,negated_conjecture,
    ( d1 = b
    | ~ product(g2,c,an_isomorphism(d2),an_isomorphism(d3)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_29]),c_0_30]) ).

cnf(c_0_57,hypothesis,
    ( d1 = b
    | X1 = d3
    | ~ product(g1,a,b,X1) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_58,hypothesis,
    product(g1,a,b,b),
    a_times_b_is_b ).

cnf(c_0_59,negated_conjecture,
    ( d1 = b
    | ~ product(g2,c,d,an_isomorphism(d3)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_55]),c_0_23]) ).

cnf(c_0_60,hypothesis,
    ( d3 = b
    | d1 = b ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_61,hypothesis,
    ( d2 = b
    | X1 = d3
    | ~ product(g1,d1,a,X1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_24]) ).

cnf(c_0_62,negated_conjecture,
    d1 = b,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_23]),c_0_31])]) ).

cnf(c_0_63,hypothesis,
    ( d2 = b
    | X1 = d3
    | ~ product(g1,b,a,X1) ),
    inference(rw,[status(thm)],[c_0_61,c_0_62]) ).

cnf(c_0_64,hypothesis,
    product(g1,b,a,b),
    b_times_a_is_b ).

cnf(c_0_65,negated_conjecture,
    ( d2 = b
    | ~ product(g2,an_isomorphism(d1),c,an_isomorphism(d3)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24]),c_0_30]) ).

cnf(c_0_66,hypothesis,
    ( d3 = b
    | d2 = b ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_67,hypothesis,
    product(g2,d,c,d),
    d_times_c_is_d ).

cnf(c_0_68,negated_conjecture,
    d2 = b,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_62]),c_0_23]),c_0_23]),c_0_67])]) ).

cnf(c_0_69,hypothesis,
    ( X1 = d3
    | ~ product(g1,b,d2,X1) ),
    inference(rw,[status(thm)],[c_0_51,c_0_62]) ).

cnf(c_0_70,negated_conjecture,
    d3 = b,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_68]),c_0_62]),c_0_23]),c_0_23]),c_0_47])]) ).

cnf(c_0_71,hypothesis,
    ( X1 = b
    | ~ product(g1,b,b,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_68]),c_0_70]) ).

cnf(c_0_72,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_43]),c_0_49]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : GRP025-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32  % Computer : n025.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon Aug 28 20:06:09 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.18/0.55  start to proof: theBenchmark
% 0.18/0.57  % Version  : CSE_E---1.5
% 0.18/0.57  % Problem  : theBenchmark.p
% 0.18/0.57  % Proof found
% 0.18/0.57  % SZS status Theorem for theBenchmark.p
% 0.18/0.57  % SZS output start Proof
% See solution above
% 0.18/0.58  % Total time : 0.014000 s
% 0.18/0.58  % SZS output end Proof
% 0.18/0.58  % Total time : 0.015000 s
%------------------------------------------------------------------------------