TSTP Solution File: GRP266-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP266-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n006.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 00:18:05 EDT 2023

% Result   : Unsatisfiable 0.67s 0.75s
% Output   : CNFRefutation 0.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   36
% Syntax   : Number of formulae    :  121 (  15 unt;  14 typ;   0 def)
%            Number of atoms       :  288 ( 287 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  289 ( 108   ~; 181   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  12 con; 0-2 aty)
%            Number of variables   :   71 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    inverse: $i > $i ).

tff(decl_25,type,
    sk_c1: $i ).

tff(decl_26,type,
    sk_c11: $i ).

tff(decl_27,type,
    sk_c10: $i ).

tff(decl_28,type,
    sk_c5: $i ).

tff(decl_29,type,
    sk_c6: $i ).

tff(decl_30,type,
    sk_c9: $i ).

tff(decl_31,type,
    sk_c8: $i ).

tff(decl_32,type,
    sk_c7: $i ).

tff(decl_33,type,
    sk_c2: $i ).

tff(decl_34,type,
    sk_c4: $i ).

tff(decl_35,type,
    sk_c3: $i ).

cnf(associativity,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).

cnf(left_inverse,axiom,
    multiply(inverse(X1),X1) = identity,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).

cnf(left_identity,axiom,
    multiply(identity,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).

cnf(prove_this_17,negated_conjecture,
    ( multiply(sk_c2,sk_c9) = sk_c10
    | multiply(sk_c6,sk_c9) = sk_c10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).

cnf(prove_this_3,negated_conjecture,
    ( multiply(sk_c1,sk_c11) = sk_c10
    | multiply(sk_c6,sk_c9) = sk_c10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).

cnf(prove_this_24,negated_conjecture,
    ( inverse(sk_c2) = sk_c9
    | multiply(sk_c6,sk_c9) = sk_c10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).

cnf(prove_this_4,negated_conjecture,
    ( multiply(sk_c1,sk_c11) = sk_c10
    | inverse(sk_c6) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).

cnf(prove_this_11,negated_conjecture,
    ( inverse(sk_c1) = sk_c11
    | inverse(sk_c6) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).

cnf(prove_this_50,negated_conjecture,
    ( multiply(X1,sk_c11) != sk_c10
    | inverse(X1) != sk_c11
    | multiply(X2,sk_c9) != sk_c10
    | inverse(X2) != sk_c9
    | multiply(sk_c10,X3) != sk_c9
    | multiply(X4,sk_c10) != X3
    | inverse(X4) != sk_c10
    | multiply(X5,sk_c11) != sk_c10
    | inverse(X5) != sk_c11
    | multiply(X6,sk_c9) != sk_c10
    | inverse(X6) != sk_c9
    | multiply(sk_c9,X7) != sk_c10
    | multiply(X8,sk_c9) != X7
    | inverse(X8) != sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).

cnf(prove_this_34,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).

cnf(prove_this_35,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | inverse(sk_c7) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).

cnf(prove_this_31,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | multiply(sk_c6,sk_c9) = sk_c10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).

cnf(prove_this_33,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | multiply(sk_c9,sk_c8) = sk_c10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).

cnf(prove_this_32,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | inverse(sk_c6) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).

cnf(prove_this_29,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | multiply(sk_c5,sk_c11) = sk_c10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).

cnf(prove_this_30,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | inverse(sk_c5) = sk_c11 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).

cnf(prove_this_48,negated_conjecture,
    ( inverse(sk_c3) = sk_c10
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).

cnf(prove_this_40,negated_conjecture,
    ( multiply(sk_c3,sk_c10) = sk_c4
    | multiply(sk_c9,sk_c8) = sk_c10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).

cnf(prove_this_41,negated_conjecture,
    ( multiply(sk_c3,sk_c10) = sk_c4
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).

cnf(prove_this_49,negated_conjecture,
    ( inverse(sk_c3) = sk_c10
    | inverse(sk_c7) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).

cnf(prove_this_47,negated_conjecture,
    ( inverse(sk_c3) = sk_c10
    | multiply(sk_c9,sk_c8) = sk_c10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).

cnf(prove_this_42,negated_conjecture,
    ( multiply(sk_c3,sk_c10) = sk_c4
    | inverse(sk_c7) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).

cnf(c_0_22,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_23,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_24,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_25,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

cnf(c_0_26,negated_conjecture,
    ( multiply(sk_c2,sk_c9) = sk_c10
    | multiply(sk_c6,sk_c9) = sk_c10 ),
    prove_this_17 ).

cnf(c_0_27,negated_conjecture,
    ( multiply(sk_c1,sk_c11) = sk_c10
    | multiply(sk_c6,sk_c9) = sk_c10 ),
    prove_this_3 ).

cnf(c_0_28,negated_conjecture,
    ( multiply(inverse(sk_c2),sk_c10) = sk_c9
    | multiply(sk_c6,sk_c9) = sk_c10 ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_29,negated_conjecture,
    ( inverse(sk_c2) = sk_c9
    | multiply(sk_c6,sk_c9) = sk_c10 ),
    prove_this_24 ).

cnf(c_0_30,negated_conjecture,
    ( multiply(inverse(sk_c6),sk_c10) = sk_c9
    | multiply(sk_c1,sk_c11) = sk_c10 ),
    inference(spm,[status(thm)],[c_0_25,c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ( multiply(sk_c1,sk_c11) = sk_c10
    | inverse(sk_c6) = sk_c9 ),
    prove_this_4 ).

cnf(c_0_32,negated_conjecture,
    ( multiply(sk_c6,sk_c9) = sk_c10
    | multiply(sk_c9,sk_c10) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,negated_conjecture,
    ( multiply(sk_c1,sk_c11) = sk_c10
    | multiply(sk_c9,sk_c10) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    ( multiply(inverse(sk_c6),sk_c10) = sk_c9
    | multiply(sk_c9,sk_c10) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_25,c_0_32]) ).

cnf(c_0_35,negated_conjecture,
    ( inverse(sk_c1) = sk_c11
    | inverse(sk_c6) = sk_c9 ),
    prove_this_11 ).

cnf(c_0_36,negated_conjecture,
    ( multiply(inverse(sk_c1),sk_c10) = sk_c11
    | multiply(sk_c9,sk_c10) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_25,c_0_33]) ).

cnf(c_0_37,negated_conjecture,
    ( multiply(sk_c9,sk_c10) = sk_c9
    | inverse(sk_c1) = sk_c11 ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_38,negated_conjecture,
    ( multiply(sk_c9,sk_c10) = sk_c9
    | multiply(sk_c11,sk_c10) = sk_c11 ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_39,negated_conjecture,
    ( multiply(X1,sk_c11) != sk_c10
    | inverse(X1) != sk_c11
    | multiply(X2,sk_c9) != sk_c10
    | inverse(X2) != sk_c9
    | multiply(sk_c10,X3) != sk_c9
    | multiply(X4,sk_c10) != X3
    | inverse(X4) != sk_c10
    | multiply(X5,sk_c11) != sk_c10
    | inverse(X5) != sk_c11
    | multiply(X6,sk_c9) != sk_c10
    | inverse(X6) != sk_c9
    | multiply(sk_c9,X7) != sk_c10
    | multiply(X8,sk_c9) != X7
    | inverse(X8) != sk_c9 ),
    prove_this_50 ).

cnf(c_0_40,negated_conjecture,
    ( multiply(sk_c9,sk_c10) = sk_c9
    | sk_c10 = identity ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_38]),c_0_23]) ).

cnf(c_0_41,negated_conjecture,
    ( multiply(sk_c10,multiply(X1,sk_c10)) != sk_c9
    | multiply(sk_c9,multiply(X2,sk_c9)) != sk_c10
    | multiply(X3,sk_c9) != sk_c10
    | multiply(X4,sk_c11) != sk_c10
    | multiply(X5,sk_c9) != sk_c10
    | multiply(X6,sk_c11) != sk_c10
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c9
    | inverse(X4) != sk_c11
    | inverse(X1) != sk_c10
    | inverse(X5) != sk_c9
    | inverse(X6) != sk_c11 ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_39])]) ).

cnf(c_0_42,negated_conjecture,
    sk_c10 = identity,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_40]),c_0_23])]) ).

cnf(c_0_43,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    prove_this_34 ).

cnf(c_0_44,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | inverse(sk_c7) = sk_c9 ),
    prove_this_35 ).

cnf(c_0_45,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | multiply(sk_c6,sk_c9) = sk_c10 ),
    prove_this_31 ).

cnf(c_0_46,negated_conjecture,
    ( multiply(sk_c9,multiply(X1,sk_c9)) != identity
    | multiply(X2,identity) != sk_c9
    | multiply(X3,sk_c9) != identity
    | multiply(X4,sk_c11) != identity
    | multiply(X5,sk_c9) != identity
    | multiply(X6,sk_c11) != identity
    | inverse(X1) != sk_c9
    | inverse(X3) != sk_c9
    | inverse(X4) != sk_c11
    | inverse(X2) != identity
    | inverse(X5) != sk_c9
    | inverse(X6) != sk_c11 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_42]),c_0_24]),c_0_42]),c_0_42]),c_0_42]),c_0_42]),c_0_42]),c_0_42]) ).

cnf(c_0_47,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | sk_c4 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_42]),c_0_24]) ).

cnf(c_0_48,negated_conjecture,
    ( inverse(sk_c7) = sk_c9
    | sk_c4 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_42]),c_0_24]) ).

cnf(c_0_49,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | multiply(sk_c9,sk_c8) = sk_c10 ),
    prove_this_33 ).

cnf(c_0_50,negated_conjecture,
    ( multiply(inverse(sk_c6),sk_c10) = sk_c9
    | multiply(sk_c10,sk_c4) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_25,c_0_45]) ).

cnf(c_0_51,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | inverse(sk_c6) = sk_c9 ),
    prove_this_32 ).

cnf(c_0_52,negated_conjecture,
    ( multiply(inverse(sk_c7),sk_c8) = sk_c9
    | multiply(sk_c10,sk_c4) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_25,c_0_43]) ).

cnf(c_0_53,negated_conjecture,
    ( sk_c4 = sk_c9
    | multiply(sk_c9,sk_c8) != identity
    | multiply(X1,identity) != sk_c9
    | multiply(X2,sk_c9) != identity
    | multiply(X3,sk_c11) != identity
    | multiply(X4,sk_c9) != identity
    | multiply(X5,sk_c11) != identity
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c11
    | inverse(X1) != identity
    | inverse(X4) != sk_c9
    | inverse(X5) != sk_c11 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).

cnf(c_0_54,negated_conjecture,
    ( multiply(sk_c9,sk_c8) = identity
    | sk_c4 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_42]),c_0_24]),c_0_42]) ).

cnf(c_0_55,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | multiply(sk_c9,sk_c10) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_56,plain,
    multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_25,c_0_25]) ).

cnf(c_0_57,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | multiply(sk_c9,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_52,c_0_44]) ).

cnf(c_0_58,negated_conjecture,
    ( sk_c4 = sk_c9
    | multiply(X1,identity) != sk_c9
    | multiply(X2,sk_c9) != identity
    | multiply(X3,sk_c11) != identity
    | multiply(X4,sk_c9) != identity
    | multiply(X5,sk_c11) != identity
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c11
    | inverse(X1) != identity
    | inverse(X4) != sk_c9
    | inverse(X5) != sk_c11 ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_59,negated_conjecture,
    ( multiply(sk_c9,identity) = sk_c9
    | sk_c4 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_42]),c_0_24]),c_0_42]) ).

cnf(c_0_60,negated_conjecture,
    ( multiply(inverse(sk_c9),identity) = sk_c8
    | sk_c4 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_25,c_0_54]) ).

cnf(c_0_61,plain,
    multiply(X1,identity) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_56]) ).

cnf(c_0_62,negated_conjecture,
    ( multiply(sk_c9,sk_c8) = sk_c9
    | sk_c4 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_42]),c_0_24]) ).

cnf(c_0_63,negated_conjecture,
    ( sk_c4 = sk_c9
    | multiply(X1,sk_c9) != identity
    | multiply(X2,sk_c11) != identity
    | multiply(X3,sk_c9) != identity
    | multiply(X4,sk_c11) != identity
    | inverse(sk_c9) != identity
    | inverse(X1) != sk_c9
    | inverse(X2) != sk_c11
    | inverse(X3) != sk_c9
    | inverse(X4) != sk_c11 ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_64,negated_conjecture,
    ( inverse(sk_c9) = sk_c8
    | sk_c4 = sk_c9 ),
    inference(rw,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_65,negated_conjecture,
    ( sk_c4 = sk_c9
    | sk_c8 = identity ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_62]),c_0_23]) ).

cnf(c_0_66,negated_conjecture,
    ( sk_c4 = sk_c9
    | multiply(X1,sk_c9) != identity
    | multiply(X2,sk_c11) != identity
    | multiply(X3,sk_c9) != identity
    | multiply(X4,sk_c11) != identity
    | inverse(X1) != sk_c9
    | inverse(X2) != sk_c11
    | inverse(X3) != sk_c9
    | inverse(X4) != sk_c11 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).

cnf(c_0_67,negated_conjecture,
    ( multiply(sk_c6,sk_c9) = identity
    | sk_c4 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_42]),c_0_24]),c_0_42]) ).

cnf(c_0_68,negated_conjecture,
    ( inverse(sk_c6) = sk_c9
    | sk_c4 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_42]),c_0_24]) ).

cnf(c_0_69,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | multiply(sk_c5,sk_c11) = sk_c10 ),
    prove_this_29 ).

cnf(c_0_70,negated_conjecture,
    ( multiply(sk_c10,sk_c4) = sk_c9
    | inverse(sk_c5) = sk_c11 ),
    prove_this_30 ).

cnf(c_0_71,negated_conjecture,
    ( sk_c4 = sk_c9
    | multiply(X1,sk_c11) != identity
    | multiply(X2,sk_c9) != identity
    | multiply(X3,sk_c11) != identity
    | inverse(X1) != sk_c11
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c11 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).

cnf(c_0_72,negated_conjecture,
    ( multiply(sk_c5,sk_c11) = identity
    | sk_c4 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_42]),c_0_24]),c_0_42]) ).

cnf(c_0_73,negated_conjecture,
    ( inverse(sk_c5) = sk_c11
    | sk_c4 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_42]),c_0_24]) ).

cnf(c_0_74,negated_conjecture,
    ( sk_c4 = sk_c9
    | multiply(X1,sk_c9) != identity
    | multiply(X2,sk_c11) != identity
    | inverse(X1) != sk_c9
    | inverse(X2) != sk_c11 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).

cnf(c_0_75,negated_conjecture,
    ( inverse(sk_c3) = sk_c10
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    prove_this_48 ).

cnf(c_0_76,negated_conjecture,
    ( multiply(sk_c3,sk_c10) = sk_c4
    | multiply(sk_c9,sk_c8) = sk_c10 ),
    prove_this_40 ).

cnf(c_0_77,negated_conjecture,
    ( multiply(sk_c3,sk_c10) = sk_c4
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    prove_this_41 ).

cnf(c_0_78,negated_conjecture,
    ( sk_c4 = sk_c9
    | multiply(X1,sk_c11) != identity
    | inverse(X1) != sk_c11 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_67]),c_0_68]) ).

cnf(c_0_79,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | multiply(sk_c10,sk_c3) = identity ),
    inference(spm,[status(thm)],[c_0_23,c_0_75]) ).

cnf(c_0_80,negated_conjecture,
    ( inverse(sk_c3) = sk_c10
    | inverse(sk_c7) = sk_c9 ),
    prove_this_49 ).

cnf(c_0_81,negated_conjecture,
    ( multiply(inverse(sk_c3),sk_c4) = sk_c10
    | multiply(sk_c9,sk_c8) = sk_c10 ),
    inference(spm,[status(thm)],[c_0_25,c_0_76]) ).

cnf(c_0_82,negated_conjecture,
    ( inverse(sk_c3) = sk_c10
    | multiply(sk_c9,sk_c8) = sk_c10 ),
    prove_this_47 ).

cnf(c_0_83,negated_conjecture,
    ( multiply(sk_c3,identity) = sk_c4
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    inference(rw,[status(thm)],[c_0_77,c_0_42]) ).

cnf(c_0_84,negated_conjecture,
    sk_c4 = sk_c9,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_73]),c_0_72]) ).

cnf(c_0_85,negated_conjecture,
    ( multiply(sk_c3,sk_c10) = sk_c4
    | inverse(sk_c7) = sk_c9 ),
    prove_this_42 ).

cnf(c_0_86,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | sk_c3 = identity ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_42]),c_0_24]) ).

cnf(c_0_87,negated_conjecture,
    ( multiply(sk_c10,sk_c3) = identity
    | inverse(sk_c7) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_23,c_0_80]) ).

cnf(c_0_88,negated_conjecture,
    ( multiply(sk_c9,sk_c8) = sk_c10
    | multiply(sk_c10,sk_c4) = sk_c10 ),
    inference(spm,[status(thm)],[c_0_81,c_0_82]) ).

cnf(c_0_89,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | sk_c3 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_61]),c_0_84]) ).

cnf(c_0_90,negated_conjecture,
    ( multiply(sk_c3,identity) = sk_c4
    | inverse(sk_c7) = sk_c9 ),
    inference(rw,[status(thm)],[c_0_85,c_0_42]) ).

cnf(c_0_91,negated_conjecture,
    ( multiply(inverse(sk_c7),sk_c8) = sk_c9
    | sk_c3 = identity ),
    inference(spm,[status(thm)],[c_0_25,c_0_86]) ).

cnf(c_0_92,negated_conjecture,
    ( inverse(sk_c7) = sk_c9
    | sk_c3 = identity ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_42]),c_0_24]) ).

cnf(c_0_93,negated_conjecture,
    ( multiply(sk_c9,sk_c8) = sk_c10
    | sk_c10 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_49,c_0_88]) ).

cnf(c_0_94,negated_conjecture,
    ( multiply(inverse(sk_c7),sk_c8) = sk_c9
    | sk_c3 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_25,c_0_89]) ).

cnf(c_0_95,negated_conjecture,
    ( inverse(sk_c7) = sk_c9
    | sk_c3 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_61]),c_0_84]) ).

cnf(c_0_96,negated_conjecture,
    ( multiply(sk_c9,sk_c8) = sk_c9
    | sk_c3 = identity ),
    inference(spm,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_97,negated_conjecture,
    ( multiply(sk_c9,sk_c8) = identity
    | sk_c9 = identity ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_42]),c_0_42]) ).

cnf(c_0_98,negated_conjecture,
    ( multiply(sk_c9,sk_c8) = sk_c9
    | sk_c3 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_94,c_0_95]) ).

cnf(c_0_99,negated_conjecture,
    ( sk_c3 = identity
    | sk_c9 = identity ),
    inference(spm,[status(thm)],[c_0_96,c_0_97]) ).

cnf(c_0_100,negated_conjecture,
    ( sk_c3 = sk_c9
    | sk_c9 = identity ),
    inference(spm,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_101,negated_conjecture,
    sk_c9 = identity,
    inference(spm,[status(thm)],[c_0_99,c_0_100]) ).

cnf(c_0_102,plain,
    inverse(identity) = identity,
    inference(spm,[status(thm)],[c_0_23,c_0_61]) ).

cnf(c_0_103,negated_conjecture,
    ( multiply(X1,sk_c11) != identity
    | multiply(X2,sk_c11) != identity
    | inverse(X1) != sk_c11
    | inverse(X2) != sk_c11 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_61])]),c_0_101]),c_0_101]),c_0_61]),c_0_24]),c_0_101]),c_0_61]),c_0_101]),c_0_61]),c_0_101]),c_0_101]),c_0_101]),c_0_102]),c_0_101])])])])]),c_0_102])]) ).

cnf(c_0_104,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_61]),c_0_61]) ).

cnf(c_0_105,negated_conjecture,
    ( multiply(X1,sk_c11) != identity
    | inverse(X1) != sk_c11 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_23]),c_0_104])]) ).

cnf(c_0_106,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_104])]),c_0_23])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GRP266-1 : TPTP v8.1.2. Released v2.5.0.
% 0.12/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Aug 28 22:45:51 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.67/0.75  % Version  : CSE_E---1.5
% 0.67/0.75  % Problem  : theBenchmark.p
% 0.67/0.75  % Proof found
% 0.67/0.75  % SZS status Theorem for theBenchmark.p
% 0.67/0.75  % SZS output start Proof
% See solution above
% 0.67/0.76  % Total time : 0.166000 s
% 0.67/0.76  % SZS output end Proof
% 0.67/0.76  % Total time : 0.169000 s
%------------------------------------------------------------------------------