TSTP Solution File: GRP239-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP239-1 : 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 : n020.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 00:17:52 EDT 2023

% Result   : Unsatisfiable 0.93s 1.06s
% Output   : CNFRefutation 1.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  151 (  25 unt;  12 typ;   0 def)
%            Number of atoms       :  339 ( 338 equ)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :  295 (  95   ~; 200   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   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    :   12 (  12 usr;  10 con; 0-2 aty)
%            Number of variables   :   66 (   1 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_c9: $i ).

tff(decl_26,type,
    sk_c8: $i ).

tff(decl_27,type,
    sk_c4: $i ).

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

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

tff(decl_30,type,
    sk_c7: $i ).

tff(decl_31,type,
    sk_c1: $i ).

tff(decl_32,type,
    sk_c3: $i ).

tff(decl_33,type,
    sk_c2: $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_16,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c9
    | multiply(sk_c4,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).

cnf(prove_this_15,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c9
    | inverse(sk_c4) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).

cnf(prove_this_9,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c4,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).

cnf(prove_this_24,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | multiply(sk_c5,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).

cnf(prove_this_8,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | inverse(sk_c4) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).

cnf(prove_this_43,negated_conjecture,
    ( inverse(sk_c9) != sk_c8
    | inverse(X1) != sk_c9
    | multiply(X1,sk_c8) != sk_c9
    | multiply(sk_c9,X2) != sk_c8
    | multiply(X3,sk_c9) != X2
    | inverse(X3) != sk_c9
    | inverse(X4) != sk_c9
    | multiply(X4,sk_c8) != sk_c9
    | multiply(X5,sk_c8) != sk_c9
    | inverse(X5) != sk_c8
    | multiply(X6,X7) != sk_c8
    | inverse(X6) != X7
    | multiply(X7,sk_c9) != sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).

cnf(prove_this_26,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | multiply(sk_c6,sk_c7) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).

cnf(prove_this_23,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | multiply(sk_c4,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).

cnf(prove_this_25,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | inverse(sk_c5) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).

cnf(prove_this_7,negated_conjecture,
    ( inverse(sk_c9) = sk_c8
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).

cnf(prove_this_21,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c9
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).

cnf(prove_this_27,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | inverse(sk_c6) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).

cnf(prove_this_35,negated_conjecture,
    ( multiply(sk_c2,sk_c9) = sk_c3
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).

cnf(prove_this_42,negated_conjecture,
    ( inverse(sk_c2) = sk_c9
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).

cnf(prove_this_28,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).

cnf(prove_this_14,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).

cnf(prove_this_33,negated_conjecture,
    ( multiply(sk_c2,sk_c9) = sk_c3
    | multiply(sk_c6,sk_c7) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).

cnf(prove_this_1,negated_conjecture,
    ( inverse(sk_c9) = sk_c8
    | inverse(sk_c4) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).

cnf(prove_this_34,negated_conjecture,
    ( multiply(sk_c2,sk_c9) = sk_c3
    | inverse(sk_c6) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).

cnf(prove_this_39,negated_conjecture,
    ( inverse(sk_c2) = sk_c9
    | inverse(sk_c5) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).

cnf(prove_this_4,negated_conjecture,
    ( inverse(sk_c9) = sk_c8
    | inverse(sk_c5) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).

cnf(prove_this_38,negated_conjecture,
    ( inverse(sk_c2) = sk_c9
    | multiply(sk_c5,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).

cnf(prove_this_3,negated_conjecture,
    ( inverse(sk_c9) = sk_c8
    | multiply(sk_c5,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).

cnf(c_0_26,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_27,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_28,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_29,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).

cnf(c_0_30,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c9
    | multiply(sk_c4,sk_c8) = sk_c9 ),
    prove_this_16 ).

cnf(c_0_31,negated_conjecture,
    ( multiply(inverse(sk_c4),sk_c9) = sk_c8
    | multiply(sk_c1,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_32,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c9
    | inverse(sk_c4) = sk_c9 ),
    prove_this_15 ).

cnf(c_0_33,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c9
    | multiply(sk_c9,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_34,negated_conjecture,
    ( multiply(inverse(sk_c1),sk_c9) = sk_c8
    | multiply(sk_c9,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_29,c_0_33]) ).

cnf(c_0_35,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c4,sk_c8) = sk_c9 ),
    prove_this_9 ).

cnf(c_0_36,negated_conjecture,
    ( multiply(sk_c4,sk_c8) = sk_c9
    | multiply(sk_c9,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_37,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | multiply(sk_c5,sk_c8) = sk_c9 ),
    prove_this_24 ).

cnf(c_0_38,negated_conjecture,
    ( multiply(inverse(sk_c4),sk_c9) = sk_c8
    | multiply(sk_c9,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_29,c_0_36]) ).

cnf(c_0_39,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | inverse(sk_c4) = sk_c9 ),
    prove_this_8 ).

cnf(c_0_40,negated_conjecture,
    ( inverse(sk_c9) != sk_c8
    | inverse(X1) != sk_c9
    | multiply(X1,sk_c8) != sk_c9
    | multiply(sk_c9,X2) != sk_c8
    | multiply(X3,sk_c9) != X2
    | inverse(X3) != sk_c9
    | inverse(X4) != sk_c9
    | multiply(X4,sk_c8) != sk_c9
    | multiply(X5,sk_c8) != sk_c9
    | inverse(X5) != sk_c8
    | multiply(X6,X7) != sk_c8
    | inverse(X6) != X7
    | multiply(X7,sk_c9) != sk_c8 ),
    prove_this_43 ).

cnf(c_0_41,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | multiply(sk_c6,sk_c7) = sk_c8 ),
    prove_this_26 ).

cnf(c_0_42,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | multiply(sk_c4,sk_c8) = sk_c9 ),
    prove_this_23 ).

cnf(c_0_43,negated_conjecture,
    ( multiply(inverse(sk_c5),sk_c9) = sk_c8
    | multiply(sk_c9,sk_c3) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_29,c_0_37]) ).

cnf(c_0_44,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | inverse(sk_c5) = sk_c8 ),
    prove_this_25 ).

cnf(c_0_45,negated_conjecture,
    ( multiply(sk_c9,sk_c9) = sk_c8
    | inverse(sk_c1) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_46,negated_conjecture,
    ( multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
    | multiply(inverse(X2),sk_c9) != sk_c8
    | multiply(X2,inverse(X2)) != sk_c8
    | multiply(X3,sk_c8) != sk_c9
    | multiply(X4,sk_c8) != sk_c9
    | multiply(X5,sk_c8) != sk_c9
    | inverse(sk_c9) != sk_c8
    | inverse(X3) != sk_c8
    | inverse(X4) != sk_c9
    | inverse(X1) != sk_c9
    | inverse(X5) != sk_c9 ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_40])]) ).

cnf(c_0_47,negated_conjecture,
    ( inverse(sk_c9) = sk_c8
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    prove_this_7 ).

cnf(c_0_48,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c9
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    prove_this_21 ).

cnf(c_0_49,negated_conjecture,
    ( multiply(inverse(sk_c6),sk_c8) = sk_c7
    | multiply(sk_c9,sk_c3) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_29,c_0_41]) ).

cnf(c_0_50,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | inverse(sk_c6) = sk_c7 ),
    prove_this_27 ).

cnf(c_0_51,negated_conjecture,
    ( multiply(sk_c4,multiply(sk_c8,X1)) = multiply(sk_c9,X1)
    | multiply(sk_c9,sk_c3) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_26,c_0_42]) ).

cnf(c_0_52,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | multiply(sk_c8,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_53,negated_conjecture,
    multiply(sk_c9,sk_c9) = sk_c8,
    inference(spm,[status(thm)],[c_0_34,c_0_45]) ).

cnf(c_0_54,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | multiply(sk_c9,multiply(X1,sk_c9)) != sk_c8
    | multiply(inverse(X2),sk_c9) != sk_c8
    | multiply(X2,inverse(X2)) != sk_c8
    | multiply(X3,sk_c8) != sk_c9
    | multiply(X4,sk_c8) != sk_c9
    | multiply(X5,sk_c8) != sk_c9
    | inverse(X3) != sk_c8
    | inverse(X4) != sk_c9
    | inverse(X1) != sk_c9
    | inverse(X5) != sk_c9 ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_55,negated_conjecture,
    ( multiply(sk_c2,sk_c9) = sk_c3
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    prove_this_35 ).

cnf(c_0_56,negated_conjecture,
    ( inverse(sk_c2) = sk_c9
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    prove_this_42 ).

cnf(c_0_57,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    prove_this_28 ).

cnf(c_0_58,negated_conjecture,
    ( multiply(inverse(sk_c1),sk_c9) = sk_c8
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_29,c_0_48]) ).

cnf(c_0_59,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    prove_this_14 ).

cnf(c_0_60,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | multiply(sk_c7,sk_c8) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_61,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | multiply(sk_c4,sk_c8) = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).

cnf(c_0_62,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | multiply(inverse(X1),sk_c9) != sk_c8
    | multiply(X1,inverse(X1)) != sk_c8
    | multiply(X2,sk_c8) != sk_c9
    | multiply(X3,sk_c8) != sk_c9
    | multiply(X4,sk_c8) != sk_c9
    | inverse(X2) != sk_c8
    | inverse(X3) != sk_c9
    | inverse(X4) != sk_c9 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57]) ).

cnf(c_0_63,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | multiply(sk_c9,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_64,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | sk_c8 = identity ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_60]),c_0_27]) ).

cnf(c_0_65,negated_conjecture,
    ( multiply(sk_c9,sk_c3) = sk_c8
    | sk_c8 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_42,c_0_61]) ).

cnf(c_0_66,negated_conjecture,
    multiply(inverse(sk_c9),sk_c8) = sk_c9,
    inference(spm,[status(thm)],[c_0_29,c_0_53]) ).

cnf(c_0_67,plain,
    multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_29,c_0_29]) ).

cnf(c_0_68,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | multiply(sk_c2,sk_c9) != sk_c8
    | multiply(X1,sk_c8) != sk_c9
    | multiply(X2,sk_c8) != sk_c9
    | multiply(X3,sk_c8) != sk_c9
    | inverse(X1) != sk_c8
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c9 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_56]),c_0_63]) ).

cnf(c_0_69,negated_conjecture,
    ( multiply(inverse(sk_c9),sk_c8) = sk_c3
    | sk_c8 = identity ),
    inference(spm,[status(thm)],[c_0_29,c_0_64]) ).

cnf(c_0_70,negated_conjecture,
    ( multiply(inverse(sk_c2),sk_c3) = sk_c9
    | multiply(sk_c7,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_29,c_0_55]) ).

cnf(c_0_71,negated_conjecture,
    ( sk_c8 = sk_c9
    | sk_c3 = sk_c9 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_65]),c_0_66]) ).

cnf(c_0_72,plain,
    multiply(X1,identity) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_67]) ).

cnf(c_0_73,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | multiply(X1,sk_c8) != sk_c9
    | multiply(X2,sk_c8) != sk_c9
    | multiply(X3,sk_c8) != sk_c9
    | inverse(X1) != sk_c8
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c9
    | sk_c3 != sk_c8 ),
    inference(spm,[status(thm)],[c_0_68,c_0_55]) ).

cnf(c_0_74,negated_conjecture,
    ( sk_c8 = identity
    | sk_c3 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_69,c_0_66]) ).

cnf(c_0_75,negated_conjecture,
    ( multiply(inverse(sk_c2),sk_c9) = sk_c9
    | multiply(sk_c7,sk_c9) = sk_c8
    | sk_c8 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_76,plain,
    inverse(identity) = identity,
    inference(spm,[status(thm)],[c_0_27,c_0_72]) ).

cnf(c_0_77,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | sk_c8 = identity
    | multiply(X1,sk_c8) != sk_c9
    | multiply(X2,sk_c8) != sk_c9
    | multiply(X3,sk_c8) != sk_c9
    | inverse(X1) != sk_c8
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c9
    | sk_c8 != sk_c9 ),
    inference(spm,[status(thm)],[c_0_73,c_0_74]) ).

cnf(c_0_78,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | sk_c8 = sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_56]),c_0_53])]) ).

cnf(c_0_79,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | multiply(X1,sk_c8) != sk_c9
    | multiply(X2,sk_c8) != sk_c9
    | multiply(X3,sk_c8) != sk_c9
    | inverse(X1) != sk_c8
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c9 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_76]),c_0_28]),c_0_72]),c_0_77]),c_0_78]) ).

cnf(c_0_80,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | multiply(X1,sk_c8) != sk_c9
    | multiply(X2,sk_c8) != sk_c9
    | inverse(sk_c1) != sk_c8
    | inverse(X1) != sk_c9
    | inverse(X2) != sk_c9 ),
    inference(spm,[status(thm)],[c_0_79,c_0_48]) ).

cnf(c_0_81,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | multiply(X1,sk_c8) != sk_c9
    | multiply(X2,sk_c8) != sk_c9
    | inverse(X1) != sk_c9
    | inverse(X2) != sk_c9 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_59]),c_0_78]) ).

cnf(c_0_82,negated_conjecture,
    ( multiply(sk_c7,sk_c9) = sk_c8
    | multiply(X1,sk_c8) != sk_c9
    | inverse(X1) != sk_c9 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_48]),c_0_59]) ).

cnf(c_0_83,negated_conjecture,
    multiply(sk_c7,sk_c9) = sk_c8,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_59]),c_0_48]) ).

cnf(c_0_84,negated_conjecture,
    ( multiply(sk_c2,sk_c9) = sk_c3
    | multiply(sk_c6,sk_c7) = sk_c8 ),
    prove_this_33 ).

cnf(c_0_85,negated_conjecture,
    multiply(sk_c7,multiply(sk_c9,X1)) = multiply(sk_c8,X1),
    inference(spm,[status(thm)],[c_0_26,c_0_83]) ).

cnf(c_0_86,negated_conjecture,
    ( inverse(sk_c9) = sk_c8
    | inverse(sk_c4) = sk_c9 ),
    prove_this_1 ).

cnf(c_0_87,negated_conjecture,
    ( multiply(inverse(sk_c6),sk_c8) = sk_c7
    | multiply(sk_c2,sk_c9) = sk_c3 ),
    inference(spm,[status(thm)],[c_0_29,c_0_84]) ).

cnf(c_0_88,negated_conjecture,
    ( multiply(sk_c2,sk_c9) = sk_c3
    | inverse(sk_c6) = sk_c7 ),
    prove_this_34 ).

cnf(c_0_89,negated_conjecture,
    multiply(sk_c7,sk_c8) = multiply(sk_c8,sk_c9),
    inference(spm,[status(thm)],[c_0_85,c_0_53]) ).

cnf(c_0_90,negated_conjecture,
    ( multiply(sk_c9,sk_c4) = identity
    | inverse(sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_27,c_0_86]) ).

cnf(c_0_91,negated_conjecture,
    ( inverse(sk_c2) = sk_c9
    | inverse(sk_c5) = sk_c8 ),
    prove_this_39 ).

cnf(c_0_92,negated_conjecture,
    ( multiply(sk_c2,sk_c9) = sk_c3
    | multiply(sk_c7,sk_c8) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_93,negated_conjecture,
    multiply(inverse(sk_c7),multiply(sk_c8,sk_c9)) = sk_c8,
    inference(spm,[status(thm)],[c_0_29,c_0_89]) ).

cnf(c_0_94,negated_conjecture,
    ( multiply(sk_c9,sk_c4) = identity
    | multiply(sk_c8,sk_c9) = identity ),
    inference(spm,[status(thm)],[c_0_27,c_0_90]) ).

cnf(c_0_95,negated_conjecture,
    ( inverse(sk_c9) = sk_c8
    | inverse(sk_c5) = sk_c8 ),
    prove_this_4 ).

cnf(c_0_96,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_72]),c_0_72]) ).

cnf(c_0_97,negated_conjecture,
    ( multiply(sk_c8,sk_c5) = identity
    | inverse(sk_c2) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_27,c_0_91]) ).

cnf(c_0_98,negated_conjecture,
    ( multiply(inverse(sk_c2),sk_c3) = sk_c9
    | multiply(sk_c7,sk_c8) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_29,c_0_92]) ).

cnf(c_0_99,negated_conjecture,
    ( multiply(sk_c9,sk_c4) = identity
    | inverse(sk_c7) = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_72]) ).

cnf(c_0_100,negated_conjecture,
    ( inverse(sk_c2) = sk_c9
    | multiply(sk_c5,sk_c8) = sk_c9 ),
    prove_this_38 ).

cnf(c_0_101,negated_conjecture,
    ( multiply(sk_c8,sk_c5) = identity
    | inverse(sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_27,c_0_95]) ).

cnf(c_0_102,negated_conjecture,
    ( multiply(sk_c8,sk_c5) = identity
    | inverse(sk_c9) = sk_c2 ),
    inference(spm,[status(thm)],[c_0_96,c_0_97]) ).

cnf(c_0_103,negated_conjecture,
    ( multiply(inverse(sk_c2),sk_c9) = sk_c9
    | multiply(sk_c7,sk_c8) = sk_c7
    | sk_c8 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_98,c_0_71]) ).

cnf(c_0_104,negated_conjecture,
    ( multiply(sk_c9,sk_c4) = identity
    | inverse(sk_c8) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_96,c_0_99]) ).

cnf(c_0_105,negated_conjecture,
    ( multiply(sk_c9,sk_c4) = identity
    | inverse(sk_c8) = sk_c9 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_94]),c_0_72]) ).

cnf(c_0_106,negated_conjecture,
    ( inverse(sk_c9) = sk_c8
    | multiply(sk_c5,sk_c8) = sk_c9 ),
    prove_this_3 ).

cnf(c_0_107,negated_conjecture,
    ( multiply(sk_c5,sk_c8) = sk_c9
    | inverse(sk_c9) = sk_c2 ),
    inference(spm,[status(thm)],[c_0_96,c_0_100]) ).

cnf(c_0_108,negated_conjecture,
    ( multiply(sk_c8,sk_c5) = identity
    | sk_c2 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_101,c_0_102]) ).

cnf(c_0_109,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c7
    | multiply(sk_c2,sk_c9) = sk_c9
    | sk_c8 = sk_c9 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_103]),c_0_67]) ).

cnf(c_0_110,negated_conjecture,
    multiply(sk_c9,multiply(sk_c9,X1)) = multiply(sk_c8,X1),
    inference(spm,[status(thm)],[c_0_26,c_0_53]) ).

cnf(c_0_111,negated_conjecture,
    ( multiply(sk_c9,sk_c4) = identity
    | sk_c7 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_104,c_0_105]) ).

cnf(c_0_112,negated_conjecture,
    ( multiply(sk_c5,sk_c8) = sk_c9
    | sk_c2 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_106,c_0_107]) ).

cnf(c_0_113,negated_conjecture,
    ( inverse(sk_c8) = sk_c5
    | sk_c2 = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_108]),c_0_72]) ).

cnf(c_0_114,negated_conjecture,
    ( multiply(sk_c2,sk_c9) = sk_c9
    | multiply(sk_c8,sk_c9) = sk_c7
    | sk_c8 = sk_c9 ),
    inference(rw,[status(thm)],[c_0_109,c_0_89]) ).

cnf(c_0_115,negated_conjecture,
    multiply(sk_c8,sk_c9) = multiply(sk_c9,sk_c8),
    inference(spm,[status(thm)],[c_0_110,c_0_53]) ).

cnf(c_0_116,negated_conjecture,
    ( multiply(sk_c8,sk_c4) = sk_c9
    | sk_c7 = sk_c9 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_72]) ).

cnf(c_0_117,negated_conjecture,
    ( multiply(sk_c8,sk_c4) = sk_c7
    | sk_c7 = sk_c9 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_111]),c_0_72]) ).

cnf(c_0_118,negated_conjecture,
    ( multiply(inverse(sk_c5),sk_c9) = sk_c8
    | sk_c2 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_29,c_0_112]) ).

cnf(c_0_119,negated_conjecture,
    ( inverse(sk_c5) = sk_c8
    | sk_c2 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_96,c_0_113]) ).

cnf(c_0_120,negated_conjecture,
    ( multiply(sk_c5,sk_c8) = sk_c9
    | multiply(sk_c8,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_66,c_0_106]) ).

cnf(c_0_121,negated_conjecture,
    ( multiply(sk_c9,sk_c8) = sk_c7
    | multiply(sk_c2,sk_c9) = sk_c9
    | sk_c8 = sk_c9 ),
    inference(rw,[status(thm)],[c_0_114,c_0_115]) ).

cnf(c_0_122,negated_conjecture,
    sk_c7 = sk_c9,
    inference(spm,[status(thm)],[c_0_116,c_0_117]) ).

cnf(c_0_123,negated_conjecture,
    ( multiply(sk_c9,sk_c8) = sk_c8
    | sk_c2 = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_115]) ).

cnf(c_0_124,negated_conjecture,
    ( multiply(inverse(sk_c5),sk_c9) = sk_c8
    | multiply(sk_c8,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_29,c_0_120]) ).

cnf(c_0_125,negated_conjecture,
    ( multiply(sk_c2,sk_c9) = sk_c9
    | multiply(sk_c9,sk_c8) = sk_c9
    | sk_c8 = sk_c9 ),
    inference(rw,[status(thm)],[c_0_121,c_0_122]) ).

cnf(c_0_126,negated_conjecture,
    ( sk_c2 = sk_c8
    | sk_c8 = sk_c9 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_123]),c_0_66]) ).

cnf(c_0_127,negated_conjecture,
    ( multiply(sk_c8,sk_c8) = sk_c9
    | multiply(sk_c8,sk_c9) = sk_c8
    | inverse(sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_124,c_0_95]) ).

cnf(c_0_128,negated_conjecture,
    ( multiply(sk_c9,sk_c8) = sk_c9
    | sk_c8 = sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_115])]) ).

cnf(c_0_129,negated_conjecture,
    ( multiply(sk_c8,sk_c9) = sk_c8
    | multiply(sk_c8,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_66,c_0_127]) ).

cnf(c_0_130,negated_conjecture,
    ( sk_c8 = sk_c9
    | sk_c8 = identity ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_128]),c_0_27]) ).

cnf(c_0_131,negated_conjecture,
    ( multiply(inverse(sk_c8),sk_c9) = sk_c8
    | multiply(sk_c8,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_29,c_0_129]) ).

cnf(c_0_132,negated_conjecture,
    ( sk_c8 = identity
    | sk_c9 != identity ),
    inference(ef,[status(thm)],[c_0_130]) ).

cnf(c_0_133,negated_conjecture,
    ( multiply(inverse(sk_c8),sk_c9) = sk_c8
    | multiply(sk_c9,sk_c8) = sk_c8 ),
    inference(rw,[status(thm)],[c_0_131,c_0_115]) ).

cnf(c_0_134,negated_conjecture,
    sk_c8 = identity,
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_130]),c_0_27]),c_0_132]) ).

cnf(c_0_135,negated_conjecture,
    sk_c9 = identity,
    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)],[c_0_133,c_0_134]),c_0_76]),c_0_28]),c_0_134]),c_0_134]),c_0_72]),c_0_134])]) ).

cnf(c_0_136,plain,
    multiply(X1,inverse(X1)) = identity,
    inference(spm,[status(thm)],[c_0_27,c_0_96]) ).

cnf(c_0_137,negated_conjecture,
    inverse(X1) != identity,
    inference(cn,[status(thm)],[inference(rw,[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(er,[status(thm)],[inference(er,[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)],[c_0_46,c_0_134]),c_0_134]),c_0_134]),c_0_134]),c_0_72]),c_0_134]),c_0_72]),c_0_134]),c_0_72]),c_0_134]),c_0_134])])])]),c_0_135]),c_0_135]),c_0_72]),c_0_28]),c_0_135]),c_0_72]),c_0_136]),c_0_135]),c_0_76]),c_0_135]),c_0_76]),c_0_135]),c_0_135])])]),c_0_76])]) ).

cnf(c_0_138,plain,
    $false,
    inference(sr,[status(thm)],[c_0_76,c_0_137]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : GRP239-1 : TPTP v8.1.2. Released v2.5.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n020.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   : Tue Aug 29 02:22:28 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 0.93/1.06  % Version  : CSE_E---1.5
% 0.93/1.06  % Problem  : theBenchmark.p
% 0.93/1.06  % Proof found
% 0.93/1.06  % SZS status Theorem for theBenchmark.p
% 0.93/1.06  % SZS output start Proof
% See solution above
% 1.01/1.07  % Total time : 0.473000 s
% 1.01/1.07  % SZS output end Proof
% 1.01/1.07  % Total time : 0.477000 s
%------------------------------------------------------------------------------