TSTP Solution File: GRP772-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP772-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n005.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 00:23:41 EDT 2023

% Result   : Unsatisfiable 0.70s 0.77s
% Output   : CNFRefutation 0.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   73 (  61 unt;  12 typ;   0 def)
%            Number of atoms       :   61 (  60 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   16 (   9   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   3 con; 0-3 aty)
%            Number of variables   :  142 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    j: $i > $i ).

tff(decl_28,type,
    eta: $i > $i ).

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

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

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

tff(decl_32,type,
    x0: $i ).

tff(decl_33,type,
    x1: $i ).

cnf(sos12,axiom,
    eta(X1) = product(i(X1),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).

cnf(sos09,axiom,
    i(X1) = difference(X1,one),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).

cnf(sos13,axiom,
    product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).

cnf(sos11,axiom,
    product(i(X1),X1) = product(X1,j(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).

cnf(sos10,axiom,
    j(X1) = quotient(one,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).

cnf(sos01,axiom,
    product(X1,one) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).

cnf(sos05,axiom,
    quotient(product(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).

cnf(sos03,axiom,
    product(X1,difference(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).

cnf(sos28,axiom,
    product(product(X1,X2),a(X3,X4,X5)) = product(X1,product(X2,a(X3,X4,X5))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos28) ).

cnf(sos06,axiom,
    product(quotient(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).

cnf(sos07,axiom,
    difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).

cnf(sos04,axiom,
    difference(X1,product(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).

cnf(sos29,axiom,
    product(a(X1,X2,X3),difference(X3,product(a(X3,X1,X2),X3))) = one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos29) ).

cnf(sos27,axiom,
    product(a(X1,X2,X3),product(X4,X5)) = product(product(a(X1,X2,X3),X4),X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos27) ).

cnf(sos31,axiom,
    a(i(X1),X2,X3) = a(j(X1),X2,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos31) ).

cnf(sos32,axiom,
    a(j(X1),X2,X3) = a(X2,X3,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos32) ).

cnf(sos30,axiom,
    a(X1,i(X2),X3) = a(X1,j(X2),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos30) ).

cnf(goals,negated_conjecture,
    a(x0,x1,x1) != a(x1,x1,x0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(c_0_18,axiom,
    eta(X1) = product(i(X1),X1),
    sos12 ).

cnf(c_0_19,axiom,
    i(X1) = difference(X1,one),
    sos09 ).

cnf(c_0_20,axiom,
    product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
    sos13 ).

cnf(c_0_21,plain,
    eta(X1) = product(difference(X1,one),X1),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_22,axiom,
    product(i(X1),X1) = product(X1,j(X1)),
    sos11 ).

cnf(c_0_23,axiom,
    j(X1) = quotient(one,X1),
    sos10 ).

cnf(c_0_24,plain,
    product(difference(difference(X1,one),one),X2) = product(product(difference(X1,one),X1),product(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_19]),c_0_19]),c_0_21]) ).

cnf(c_0_25,plain,
    product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_19]),c_0_23]) ).

cnf(c_0_26,plain,
    product(product(X1,quotient(one,X1)),product(X1,X2)) = product(difference(difference(X1,one),one),X2),
    inference(rw,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_27,axiom,
    product(X1,one) = X1,
    sos01 ).

cnf(c_0_28,axiom,
    quotient(product(X1,X2),X2) = X1,
    sos05 ).

cnf(c_0_29,axiom,
    product(X1,difference(X1,X2)) = X2,
    sos03 ).

cnf(c_0_30,axiom,
    product(product(X1,X2),a(X3,X4,X5)) = product(X1,product(X2,a(X3,X4,X5))),
    sos28 ).

cnf(c_0_31,plain,
    product(product(X1,quotient(one,X1)),X1) = difference(difference(X1,one),one),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_27]) ).

cnf(c_0_32,axiom,
    product(quotient(X1,X2),X2) = X1,
    sos06 ).

cnf(c_0_33,axiom,
    difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
    sos07 ).

cnf(c_0_34,plain,
    quotient(X1,difference(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_35,plain,
    difference(difference(a(X1,X2,X3),one),one) = a(X1,X2,X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_27]) ).

cnf(c_0_36,axiom,
    difference(X1,product(X1,X2)) = X2,
    sos04 ).

cnf(c_0_37,axiom,
    product(a(X1,X2,X3),difference(X3,product(a(X3,X1,X2),X3))) = one,
    sos29 ).

cnf(c_0_38,plain,
    difference(X1,product(product(X1,X2),quotient(X3,X1))) = quotient(product(X2,X3),X1),
    inference(spm,[status(thm)],[c_0_33,c_0_32]) ).

cnf(c_0_39,plain,
    quotient(one,a(X1,X2,X3)) = difference(a(X1,X2,X3),one),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_40,axiom,
    product(a(X1,X2,X3),product(X4,X5)) = product(product(a(X1,X2,X3),X4),X5),
    sos27 ).

cnf(c_0_41,axiom,
    a(i(X1),X2,X3) = a(j(X1),X2,X3),
    sos31 ).

cnf(c_0_42,axiom,
    a(j(X1),X2,X3) = a(X2,X3,X1),
    sos32 ).

cnf(c_0_43,plain,
    difference(X1,product(a(X1,X2,X3),X1)) = difference(a(X2,X3,X1),one),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_44,plain,
    product(X1,difference(a(X2,X3,X4),one)) = quotient(X1,a(X2,X3,X4)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_36]),c_0_27]) ).

cnf(c_0_45,axiom,
    a(X1,i(X2),X3) = a(X1,j(X2),X3),
    sos30 ).

cnf(c_0_46,plain,
    a(quotient(one,X1),X2,X3) = a(difference(X1,one),X2,X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_19]),c_0_23]) ).

cnf(c_0_47,plain,
    a(quotient(one,X1),X2,X3) = a(X2,X3,X1),
    inference(rw,[status(thm)],[c_0_42,c_0_23]) ).

cnf(c_0_48,plain,
    quotient(X1,a(X2,X3,X1)) = product(a(X1,X2,X3),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_43]),c_0_44]) ).

cnf(c_0_49,plain,
    a(X1,quotient(one,X2),X3) = a(X1,difference(X2,one),X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_19]),c_0_23]) ).

cnf(c_0_50,plain,
    a(difference(X1,one),X2,X3) = a(X2,X3,X1),
    inference(rw,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_51,plain,
    difference(quotient(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_36,c_0_32]) ).

cnf(c_0_52,plain,
    product(a(X1,difference(X2,one),X3),X1) = quotient(X1,a(X3,X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_47]),c_0_49]) ).

cnf(c_0_53,plain,
    a(X1,X2,quotient(one,X3)) = a(X3,X1,X2),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_54,plain,
    a(X1,X2,difference(X3,one)) = a(X3,X1,X2),
    inference(spm,[status(thm)],[c_0_47,c_0_34]) ).

cnf(c_0_55,plain,
    quotient(X1,a(X1,X2,X3)) = product(a(X2,X3,X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_47]) ).

cnf(c_0_56,plain,
    difference(product(a(X1,X2,X3),X1),X1) = a(X2,X3,X1),
    inference(spm,[status(thm)],[c_0_51,c_0_48]) ).

cnf(c_0_57,plain,
    difference(product(a(X1,X2,X3),X3),X3) = a(X3,X1,X2),
    inference(spm,[status(thm)],[c_0_51,c_0_55]) ).

cnf(c_0_58,negated_conjecture,
    a(x0,x1,x1) != a(x1,x1,x0),
    goals ).

cnf(c_0_59,plain,
    a(X1,X1,X2) = a(X2,X1,X1),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_60,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GRP772-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n005.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 29 01:08:53 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.70/0.77  % Version  : CSE_E---1.5
% 0.70/0.77  % Problem  : theBenchmark.p
% 0.70/0.77  % Proof found
% 0.70/0.77  % SZS status Theorem for theBenchmark.p
% 0.70/0.77  % SZS output start Proof
% See solution above
% 0.70/0.77  % Total time : 0.185000 s
% 0.70/0.77  % SZS output end Proof
% 0.70/0.77  % Total time : 0.188000 s
%------------------------------------------------------------------------------