TSTP Solution File: GRP308-1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : GRP308-1 : TPTP v8.2.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n023.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 : Mon May 20 20:47:24 EDT 2024

% Result   : Unsatisfiable 2.86s 0.81s
% Output   : CNFRefutation 2.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   28
% Syntax   : Number of clauses     :  211 (  28 unt; 158 nHn; 184 RR)
%            Number of literals    :  566 ( 565 equ; 197 neg)
%            Maximal clause size   :   12 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :  124 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
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_3,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | multiply(sk_c4,sk_c7) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).

cnf(prove_this_1,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).

cnf(prove_this_4,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | inverse(sk_c4) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).

cnf(prove_this_2,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | inverse(sk_c3) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).

cnf(prove_this_6,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | multiply(sk_c5,sk_c8) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).

cnf(prove_this_5,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | inverse(sk_c5) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).

cnf(prove_this_32,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c3) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).

cnf(prove_this_13,negated_conjecture,
    ( multiply(sk_c6,sk_c7) = sk_c8
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).

cnf(prove_this_31,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).

cnf(prove_this_8,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | inverse(sk_c3) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).

cnf(prove_this_14,negated_conjecture,
    ( multiply(sk_c6,sk_c7) = sk_c8
    | inverse(sk_c3) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).

cnf(prove_this_7,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).

cnf(prove_this_21,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | multiply(sk_c4,sk_c7) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).

cnf(prove_this_37,negated_conjecture,
    ( multiply(sk_c8,sk_c7) != sk_c6
    | inverse(sk_c8) != sk_c6
    | multiply(sk_c6,sk_c7) != sk_c8
    | multiply(sk_c8,X1) != sk_c7
    | multiply(X2,sk_c8) != X1
    | inverse(X2) != sk_c8
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X3) != sk_c8
    | multiply(X4,sk_c7) != sk_c6
    | inverse(X4) != sk_c7
    | inverse(X5) != sk_c6
    | multiply(X5,sk_c8) != sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).

cnf(prove_this_34,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c4) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).

cnf(prove_this_22,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | inverse(sk_c4) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).

cnf(prove_this_10,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | inverse(sk_c4) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).

cnf(prove_this_24,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | multiply(sk_c5,sk_c8) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).

cnf(prove_this_28,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c2
    | inverse(sk_c4) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).

cnf(prove_this_23,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | inverse(sk_c5) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).

cnf(prove_this_25,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c2
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).

cnf(prove_this_19,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).

cnf(prove_this_27,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c2
    | multiply(sk_c4,sk_c7) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).

cnf(prove_this_33,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | multiply(sk_c4,sk_c7) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).

cnf(prove_this_20,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | inverse(sk_c3) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).

cnf(c_0_28,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_29,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_30,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_31,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).

cnf(c_0_32,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | multiply(sk_c4,sk_c7) = sk_c6 ),
    prove_this_3 ).

cnf(c_0_33,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    prove_this_1 ).

cnf(c_0_34,negated_conjecture,
    ( multiply(inverse(sk_c4),sk_c6) = sk_c7
    | multiply(sk_c8,sk_c7) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_35,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | inverse(sk_c4) = sk_c7 ),
    prove_this_4 ).

cnf(c_0_36,plain,
    multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_31,c_0_31]) ).

cnf(c_0_37,negated_conjecture,
    ( multiply(inverse(sk_c3),sk_c7) = sk_c8
    | multiply(sk_c8,sk_c7) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_31,c_0_33]) ).

cnf(c_0_38,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | inverse(sk_c3) = sk_c8 ),
    prove_this_2 ).

cnf(c_0_39,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | multiply(sk_c5,sk_c8) = sk_c6 ),
    prove_this_6 ).

cnf(c_0_40,negated_conjecture,
    ( multiply(sk_c4,multiply(sk_c7,X1)) = multiply(sk_c6,X1)
    | multiply(sk_c8,sk_c7) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_28,c_0_32]) ).

cnf(c_0_41,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | multiply(sk_c7,sk_c6) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_42,plain,
    multiply(X1,identity) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_29]),c_0_36]) ).

cnf(c_0_43,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | multiply(sk_c8,sk_c7) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_44,negated_conjecture,
    ( multiply(inverse(sk_c5),sk_c6) = sk_c8
    | multiply(sk_c8,sk_c7) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_31,c_0_39]) ).

cnf(c_0_45,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | inverse(sk_c5) = sk_c6 ),
    prove_this_5 ).

cnf(c_0_46,negated_conjecture,
    ( multiply(sk_c4,sk_c7) = multiply(sk_c6,sk_c6)
    | multiply(sk_c8,sk_c7) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_47,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_42]),c_0_42]) ).

cnf(c_0_48,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c3) = sk_c8 ),
    prove_this_32 ).

cnf(c_0_49,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c8
    | sk_c6 != sk_c8 ),
    inference(ef,[status(thm)],[c_0_43]) ).

cnf(c_0_50,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | multiply(sk_c6,sk_c6) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_51,negated_conjecture,
    ( multiply(sk_c7,multiply(sk_c6,X1)) = multiply(sk_c7,X1)
    | multiply(sk_c8,sk_c7) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_28,c_0_41]) ).

cnf(c_0_52,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | multiply(sk_c6,sk_c5) = identity ),
    inference(spm,[status(thm)],[c_0_29,c_0_45]) ).

cnf(c_0_53,negated_conjecture,
    ( multiply(sk_c6,sk_c6) = sk_c6
    | multiply(sk_c8,sk_c7) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_32,c_0_46]) ).

cnf(c_0_54,negated_conjecture,
    ( inverse(sk_c3) = sk_c8
    | inverse(sk_c8) = sk_c1 ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_55,negated_conjecture,
    ( multiply(sk_c6,sk_c7) = sk_c8
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    prove_this_13 ).

cnf(c_0_56,plain,
    inverse(identity) = identity,
    inference(spm,[status(thm)],[c_0_29,c_0_42]) ).

cnf(c_0_57,negated_conjecture,
    ( identity = sk_c7
    | sk_c6 != sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_49]),c_0_29]) ).

cnf(c_0_58,negated_conjecture,
    ( multiply(sk_c6,multiply(sk_c6,X1)) = multiply(sk_c8,X1)
    | multiply(sk_c8,sk_c7) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_28,c_0_50]) ).

cnf(c_0_59,negated_conjecture,
    ( multiply(sk_c8,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
    | sk_c6 != sk_c8 ),
    inference(spm,[status(thm)],[c_0_28,c_0_49]) ).

cnf(c_0_60,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | multiply(sk_c7,sk_c5) = sk_c7 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_42]) ).

cnf(c_0_61,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_50,c_0_53]) ).

cnf(c_0_62,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    prove_this_31 ).

cnf(c_0_63,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | inverse(sk_c3) = sk_c8 ),
    prove_this_8 ).

cnf(c_0_64,negated_conjecture,
    ( inverse(sk_c8) = sk_c1
    | inverse(sk_c8) = sk_c3 ),
    inference(spm,[status(thm)],[c_0_47,c_0_54]) ).

cnf(c_0_65,negated_conjecture,
    ( multiply(inverse(sk_c3),sk_c7) = sk_c8
    | multiply(sk_c6,sk_c7) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_31,c_0_55]) ).

cnf(c_0_66,negated_conjecture,
    ( inverse(sk_c7) = sk_c7
    | sk_c6 != sk_c8 ),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_67,negated_conjecture,
    ( multiply(sk_c6,sk_c7) = sk_c8
    | inverse(sk_c3) = sk_c8 ),
    prove_this_14 ).

cnf(c_0_68,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | multiply(sk_c8,sk_c5) = sk_c6 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_52]),c_0_42]) ).

cnf(c_0_69,negated_conjecture,
    ( multiply(sk_c8,sk_c5) = multiply(sk_c8,sk_c7)
    | multiply(sk_c8,sk_c7) = sk_c6 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).

cnf(c_0_70,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    prove_this_7 ).

cnf(c_0_71,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | inverse(sk_c8) = sk_c1 ),
    inference(spm,[status(thm)],[c_0_47,c_0_62]) ).

cnf(c_0_72,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | inverse(sk_c8) = sk_c3 ),
    inference(spm,[status(thm)],[c_0_47,c_0_63]) ).

cnf(c_0_73,negated_conjecture,
    ( inverse(sk_c8) = sk_c3
    | sk_c1 != sk_c3 ),
    inference(ef,[status(thm)],[c_0_64]) ).

cnf(c_0_74,negated_conjecture,
    ( multiply(inverse(sk_c3),multiply(sk_c7,X1)) = multiply(sk_c8,X1)
    | multiply(sk_c6,sk_c7) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_28,c_0_65]) ).

cnf(c_0_75,negated_conjecture,
    ( multiply(sk_c7,sk_c7) = identity
    | sk_c6 != sk_c8 ),
    inference(spm,[status(thm)],[c_0_29,c_0_66]) ).

cnf(c_0_76,negated_conjecture,
    ( multiply(sk_c6,sk_c7) = sk_c8
    | multiply(sk_c8,sk_c7) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_65,c_0_67]) ).

cnf(c_0_77,negated_conjecture,
    multiply(sk_c8,sk_c7) = sk_c6,
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_78,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | sk_c1 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_79,negated_conjecture,
    ( inverse(sk_c8) = sk_c3
    | sk_c1 = sk_c6 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_64]),c_0_73]) ).

cnf(c_0_80,negated_conjecture,
    ( inverse(sk_c3) = multiply(sk_c8,sk_c7)
    | multiply(sk_c6,sk_c7) = sk_c8
    | sk_c6 != sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_42]) ).

cnf(c_0_81,negated_conjecture,
    ( multiply(sk_c6,sk_c7) = sk_c8
    | sk_c6 = sk_c8 ),
    inference(rw,[status(thm)],[c_0_76,c_0_77]) ).

cnf(c_0_82,negated_conjecture,
    ( multiply(inverse(sk_c3),sk_c7) = sk_c8
    | sk_c1 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_31,c_0_78]) ).

cnf(c_0_83,negated_conjecture,
    ( inverse(sk_c3) = sk_c8
    | sk_c1 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_47,c_0_79]) ).

cnf(c_0_84,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | multiply(sk_c4,sk_c7) = sk_c6 ),
    prove_this_21 ).

cnf(c_0_85,negated_conjecture,
    ( multiply(sk_c8,sk_c7) != sk_c6
    | inverse(sk_c8) != sk_c6
    | multiply(sk_c6,sk_c7) != sk_c8
    | multiply(sk_c8,X1) != sk_c7
    | multiply(X2,sk_c8) != X1
    | inverse(X2) != sk_c8
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X3) != sk_c8
    | multiply(X4,sk_c7) != sk_c6
    | inverse(X4) != sk_c7
    | inverse(X5) != sk_c6
    | multiply(X5,sk_c8) != sk_c6 ),
    inference(fof_simplification,[status(thm)],[prove_this_37]) ).

cnf(c_0_86,negated_conjecture,
    ( multiply(inverse(sk_c8),sk_c6) = sk_c7
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_31,c_0_61]) ).

cnf(c_0_87,negated_conjecture,
    ( multiply(sk_c6,sk_c7) = sk_c8
    | inverse(sk_c3) = sk_c6 ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_77]),c_0_81]) ).

cnf(c_0_88,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c8
    | sk_c1 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

cnf(c_0_89,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c4) = sk_c7 ),
    prove_this_34 ).

cnf(c_0_90,negated_conjecture,
    ( multiply(inverse(sk_c4),sk_c6) = sk_c7
    | multiply(sk_c8,sk_c2) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_31,c_0_84]) ).

cnf(c_0_91,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | inverse(sk_c4) = sk_c7 ),
    prove_this_22 ).

cnf(c_0_92,negated_conjecture,
    ( multiply(sk_c8,sk_c7) != sk_c6
    | inverse(sk_c8) != sk_c6
    | multiply(sk_c6,sk_c7) != sk_c8
    | multiply(sk_c8,X1) != sk_c7
    | multiply(X2,sk_c8) != X1
    | inverse(X2) != sk_c8
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X3) != sk_c8
    | multiply(X4,sk_c7) != sk_c6
    | inverse(X4) != sk_c7
    | inverse(X5) != sk_c6
    | multiply(X5,sk_c8) != sk_c6 ),
    c_0_85 ).

cnf(c_0_93,negated_conjecture,
    ( multiply(inverse(sk_c8),multiply(sk_c6,X1)) = multiply(sk_c7,X1)
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_28,c_0_86]) ).

cnf(c_0_94,negated_conjecture,
    multiply(sk_c6,sk_c7) = sk_c8,
    inference(spm,[status(thm)],[c_0_65,c_0_87]) ).

cnf(c_0_95,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | inverse(sk_c4) = sk_c7 ),
    prove_this_10 ).

cnf(c_0_96,negated_conjecture,
    ( sk_c1 = sk_c6
    | identity = sk_c7 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_88]),c_0_29]) ).

cnf(c_0_97,negated_conjecture,
    ( inverse(sk_c4) = sk_c7
    | inverse(sk_c8) = sk_c1 ),
    inference(spm,[status(thm)],[c_0_47,c_0_89]) ).

cnf(c_0_98,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | multiply(sk_c5,sk_c8) = sk_c6 ),
    prove_this_24 ).

cnf(c_0_99,negated_conjecture,
    ( multiply(sk_c4,multiply(sk_c7,X1)) = multiply(sk_c6,X1)
    | multiply(sk_c8,sk_c2) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_28,c_0_84]) ).

cnf(c_0_100,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | multiply(sk_c7,sk_c6) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_90,c_0_91]) ).

cnf(c_0_101,negated_conjecture,
    ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
    | multiply(sk_c8,sk_c7) != sk_c6
    | multiply(sk_c6,sk_c7) != sk_c8
    | multiply(X2,sk_c8) != sk_c6
    | multiply(X3,sk_c7) != sk_c6
    | multiply(X4,sk_c8) != sk_c7
    | inverse(sk_c8) != sk_c6
    | inverse(X2) != sk_c6
    | inverse(X3) != sk_c7
    | inverse(X4) != sk_c8
    | inverse(X1) != sk_c8 ),
    inference(er,[status(thm)],[c_0_92]) ).

cnf(c_0_102,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c2
    | inverse(sk_c4) = sk_c7 ),
    prove_this_28 ).

cnf(c_0_103,negated_conjecture,
    multiply(sk_c7,sk_c7) = identity,
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_29]),c_0_75]) ).

cnf(c_0_104,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | inverse(sk_c7) = sk_c4 ),
    inference(spm,[status(thm)],[c_0_47,c_0_95]) ).

cnf(c_0_105,negated_conjecture,
    ( inverse(sk_c7) = sk_c7
    | sk_c1 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_56,c_0_96]) ).

cnf(c_0_106,negated_conjecture,
    ( inverse(sk_c8) = sk_c1
    | inverse(sk_c7) = sk_c4 ),
    inference(spm,[status(thm)],[c_0_47,c_0_97]) ).

cnf(c_0_107,negated_conjecture,
    ( multiply(inverse(sk_c5),sk_c6) = sk_c8
    | multiply(sk_c8,sk_c2) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_31,c_0_98]) ).

cnf(c_0_108,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | inverse(sk_c5) = sk_c6 ),
    prove_this_23 ).

cnf(c_0_109,negated_conjecture,
    ( multiply(sk_c4,sk_c7) = multiply(sk_c6,sk_c6)
    | multiply(sk_c8,sk_c2) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_99,c_0_100]) ).

cnf(c_0_110,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
    | multiply(X2,sk_c8) != sk_c6
    | multiply(X3,sk_c7) != sk_c6
    | multiply(X4,sk_c8) != sk_c7
    | inverse(X2) != sk_c6
    | inverse(X3) != sk_c7
    | inverse(X4) != sk_c8
    | inverse(X1) != sk_c8 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_70]),c_0_55]),c_0_33]) ).

cnf(c_0_111,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c2
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    prove_this_25 ).

cnf(c_0_112,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    prove_this_19 ).

cnf(c_0_113,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c2
    | inverse(sk_c7) = sk_c4 ),
    inference(spm,[status(thm)],[c_0_47,c_0_102]) ).

cnf(c_0_114,negated_conjecture,
    inverse(sk_c7) = sk_c7,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_103]),c_0_42]) ).

cnf(c_0_115,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | sk_c1 = sk_c6
    | sk_c4 = sk_c7 ),
    inference(spm,[status(thm)],[c_0_104,c_0_105]) ).

cnf(c_0_116,negated_conjecture,
    ( inverse(sk_c8) = sk_c1
    | sk_c1 = sk_c6
    | sk_c4 = sk_c7 ),
    inference(spm,[status(thm)],[c_0_106,c_0_105]) ).

cnf(c_0_117,negated_conjecture,
    ( multiply(sk_c7,sk_c4) = identity
    | inverse(sk_c8) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_29,c_0_95]) ).

cnf(c_0_118,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | multiply(sk_c6,sk_c6) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_107,c_0_108]) ).

cnf(c_0_119,negated_conjecture,
    ( multiply(sk_c6,sk_c6) = sk_c6
    | multiply(sk_c8,sk_c2) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_84,c_0_109]) ).

cnf(c_0_120,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | multiply(X1,sk_c8) != sk_c6
    | multiply(X2,sk_c7) != sk_c6
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X1) != sk_c6
    | inverse(X2) != sk_c7
    | inverse(X3) != sk_c8 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_62]),c_0_112]) ).

cnf(c_0_121,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c2
    | multiply(sk_c4,sk_c7) = sk_c6 ),
    prove_this_27 ).

cnf(c_0_122,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c2
    | sk_c4 = sk_c7 ),
    inference(spm,[status(thm)],[c_0_113,c_0_114]) ).

cnf(c_0_123,negated_conjecture,
    ( sk_c4 = sk_c7
    | sk_c1 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_115,c_0_116]) ).

cnf(c_0_124,negated_conjecture,
    ( multiply(sk_c7,sk_c4) = identity
    | multiply(sk_c6,sk_c8) = identity ),
    inference(spm,[status(thm)],[c_0_29,c_0_117]) ).

cnf(c_0_125,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | inverse(sk_c7) = sk_c4 ),
    inference(spm,[status(thm)],[c_0_47,c_0_91]) ).

cnf(c_0_126,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_118,c_0_119]) ).

cnf(c_0_127,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | multiply(X1,multiply(X2,sk_c8)) != sk_c6
    | inverse(multiply(X1,X2)) != sk_c6
    | multiply(X3,sk_c7) != sk_c6
    | multiply(X4,sk_c8) != sk_c7
    | inverse(X3) != sk_c7
    | inverse(X4) != sk_c8 ),
    inference(spm,[status(thm)],[c_0_120,c_0_28]) ).

cnf(c_0_128,negated_conjecture,
    ( multiply(inverse(sk_c1),sk_c2) = sk_c8
    | multiply(sk_c4,sk_c7) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_31,c_0_121]) ).

cnf(c_0_129,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | multiply(sk_c4,sk_c7) = sk_c6 ),
    prove_this_33 ).

cnf(c_0_130,negated_conjecture,
    ( multiply(sk_c6,sk_c8) = sk_c2
    | sk_c4 = sk_c7 ),
    inference(spm,[status(thm)],[c_0_122,c_0_123]) ).

cnf(c_0_131,negated_conjecture,
    ( multiply(sk_c6,sk_c8) = identity
    | sk_c4 = sk_c7 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_124]),c_0_42]),c_0_114]) ).

cnf(c_0_132,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | sk_c4 = sk_c7 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_125]),c_0_126]) ).

cnf(c_0_133,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | inverse(multiply(X1,sk_c1)) != sk_c6
    | multiply(X1,sk_c2) != sk_c6
    | multiply(X2,sk_c7) != sk_c6
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X2) != sk_c7
    | inverse(X3) != sk_c8 ),
    inference(spm,[status(thm)],[c_0_127,c_0_111]) ).

cnf(c_0_134,negated_conjecture,
    ( multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c6,X1)
    | multiply(sk_c8,sk_c2) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_28,c_0_98]) ).

cnf(c_0_135,negated_conjecture,
    ( multiply(inverse(sk_c3),sk_c7) = sk_c8
    | multiply(sk_c8,sk_c2) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_31,c_0_112]) ).

cnf(c_0_136,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | inverse(sk_c3) = sk_c8 ),
    prove_this_20 ).

cnf(c_0_137,negated_conjecture,
    ( multiply(sk_c4,sk_c7) = sk_c6
    | multiply(sk_c8,sk_c2) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_128,c_0_129]) ).

cnf(c_0_138,negated_conjecture,
    ( sk_c4 = sk_c7
    | identity = sk_c2 ),
    inference(spm,[status(thm)],[c_0_130,c_0_131]) ).

cnf(c_0_139,negated_conjecture,
    ( multiply(inverse(sk_c8),sk_c7) = sk_c2
    | sk_c4 = sk_c7 ),
    inference(spm,[status(thm)],[c_0_31,c_0_132]) ).

cnf(c_0_140,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | sk_c4 = sk_c7 ),
    inference(spm,[status(thm)],[c_0_104,c_0_114]) ).

cnf(c_0_141,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | inverse(multiply(X1,multiply(X2,sk_c1))) != sk_c6
    | multiply(X1,multiply(X2,sk_c2)) != sk_c6
    | multiply(X3,sk_c7) != sk_c6
    | multiply(X4,sk_c8) != sk_c7
    | inverse(X3) != sk_c7
    | inverse(X4) != sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_28]),c_0_28]) ).

cnf(c_0_142,negated_conjecture,
    ( multiply(sk_c5,sk_c8) = multiply(sk_c6,sk_c7)
    | multiply(sk_c8,sk_c2) = sk_c7 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_49]),c_0_126]) ).

cnf(c_0_143,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | multiply(sk_c8,sk_c7) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_135,c_0_136]) ).

cnf(c_0_144,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | multiply(sk_c6,sk_c7) = sk_c4 ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_75]),c_0_42]),c_0_126]) ).

cnf(c_0_145,negated_conjecture,
    ( multiply(sk_c4,multiply(sk_c7,X1)) = multiply(sk_c6,X1)
    | multiply(sk_c8,sk_c2) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_28,c_0_137]) ).

cnf(c_0_146,negated_conjecture,
    ( inverse(sk_c2) = sk_c2
    | sk_c4 = sk_c7 ),
    inference(spm,[status(thm)],[c_0_56,c_0_138]) ).

cnf(c_0_147,negated_conjecture,
    ( sk_c4 = sk_c7
    | sk_c2 = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_94]) ).

cnf(c_0_148,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | multiply(X1,multiply(inverse(sk_c1),sk_c2)) != sk_c6
    | inverse(multiply(X1,identity)) != sk_c6
    | multiply(X2,sk_c7) != sk_c6
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X2) != sk_c7
    | inverse(X3) != sk_c8 ),
    inference(spm,[status(thm)],[c_0_141,c_0_29]) ).

cnf(c_0_149,negated_conjecture,
    ( multiply(sk_c6,sk_c7) = sk_c6
    | multiply(sk_c8,sk_c2) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_98,c_0_142]) ).

cnf(c_0_150,negated_conjecture,
    ( multiply(sk_c5,multiply(sk_c8,X1)) = multiply(sk_c6,X1)
    | multiply(sk_c8,sk_c7) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_28,c_0_39]) ).

cnf(c_0_151,negated_conjecture,
    ( multiply(inverse(sk_c8),sk_c7) = sk_c2
    | multiply(sk_c8,sk_c7) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_31,c_0_143]) ).

cnf(c_0_152,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | sk_c4 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_144,c_0_94]) ).

cnf(c_0_153,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c8
    | sk_c4 = sk_c8 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_103]),c_0_42]),c_0_94]) ).

cnf(c_0_154,negated_conjecture,
    ( inverse(sk_c8) = sk_c8
    | sk_c4 = sk_c7 ),
    inference(spm,[status(thm)],[c_0_146,c_0_147]) ).

cnf(c_0_155,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | multiply(X1,multiply(sk_c8,sk_c2)) != sk_c6
    | inverse(multiply(X1,identity)) != sk_c6
    | multiply(X2,sk_c7) != sk_c6
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X2) != sk_c7
    | inverse(X3) != sk_c8 ),
    inference(spm,[status(thm)],[c_0_148,c_0_62]) ).

cnf(c_0_156,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | identity = sk_c6 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_100]),c_0_29]) ).

cnf(c_0_157,negated_conjecture,
    ( multiply(sk_c8,sk_c2) = sk_c7
    | identity = sk_c7 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_149]),c_0_29]) ).

cnf(c_0_158,negated_conjecture,
    ( multiply(sk_c5,sk_c8) = multiply(sk_c6,sk_c7)
    | multiply(sk_c8,sk_c7) = sk_c6 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_49]),c_0_61]) ).

cnf(c_0_159,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | multiply(sk_c8,sk_c7) = sk_c8
    | multiply(sk_c6,sk_c7) = sk_c2 ),
    inference(spm,[status(thm)],[c_0_151,c_0_70]) ).

cnf(c_0_160,negated_conjecture,
    ( sk_c4 = sk_c8
    | sk_c7 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_152,c_0_153]) ).

cnf(c_0_161,negated_conjecture,
    ( sk_c4 = sk_c7
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_140,c_0_154]) ).

cnf(c_0_162,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | identity = sk_c6
    | inverse(multiply(X1,identity)) != sk_c6
    | multiply(X1,sk_c7) != sk_c6
    | multiply(X2,sk_c7) != sk_c6
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X2) != sk_c7
    | inverse(X3) != sk_c8 ),
    inference(spm,[status(thm)],[c_0_155,c_0_156]) ).

cnf(c_0_163,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | identity = sk_c7
    | inverse(multiply(X1,identity)) != sk_c6
    | multiply(X1,sk_c7) != sk_c6
    | multiply(X2,sk_c7) != sk_c6
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X2) != sk_c7
    | inverse(X3) != sk_c8 ),
    inference(spm,[status(thm)],[c_0_155,c_0_157]) ).

cnf(c_0_164,negated_conjecture,
    ( multiply(sk_c6,sk_c7) = sk_c6
    | multiply(sk_c8,sk_c7) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_39,c_0_158]) ).

cnf(c_0_165,negated_conjecture,
    ( multiply(sk_c8,multiply(sk_c3,X1)) = X1
    | inverse(sk_c8) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_31,c_0_63]) ).

cnf(c_0_166,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | sk_c2 = sk_c8
    | sk_c6 = sk_c8 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_77]),c_0_94]) ).

cnf(c_0_167,negated_conjecture,
    ( sk_c6 = sk_c8
    | sk_c7 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_160,c_0_161]) ).

cnf(c_0_168,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | inverse(multiply(X1,identity)) != sk_c6
    | multiply(X1,sk_c8) != sk_c6
    | multiply(X2,sk_c7) != sk_c6
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X2) != sk_c7
    | inverse(X3) != sk_c8 ),
    inference(spm,[status(thm)],[c_0_127,c_0_30]) ).

cnf(c_0_169,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | identity = sk_c6
    | multiply(X1,sk_c7) != sk_c6
    | multiply(X2,sk_c7) != sk_c6
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X1) != sk_c6
    | inverse(X2) != sk_c7
    | inverse(X3) != sk_c8 ),
    inference(rw,[status(thm)],[c_0_162,c_0_42]) ).

cnf(c_0_170,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | identity = sk_c6 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_41]),c_0_29]) ).

cnf(c_0_171,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | sk_c6 = sk_c8
    | inverse(multiply(X1,identity)) != sk_c6
    | multiply(X1,sk_c7) != sk_c6
    | multiply(X2,sk_c7) != sk_c6
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X2) != sk_c7
    | inverse(X3) != sk_c8 ),
    inference(spm,[status(thm)],[c_0_155,c_0_126]) ).

cnf(c_0_172,negated_conjecture,
    ( multiply(inverse(inverse(sk_c8)),sk_c7) = sk_c6
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_31,c_0_86]) ).

cnf(c_0_173,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | identity = sk_c7
    | multiply(X1,sk_c7) != sk_c6
    | multiply(X2,sk_c7) != sk_c6
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X1) != sk_c6
    | inverse(X2) != sk_c7
    | inverse(X3) != sk_c8 ),
    inference(rw,[status(thm)],[c_0_163,c_0_42]) ).

cnf(c_0_174,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | identity = sk_c7 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_164]),c_0_29]) ).

cnf(c_0_175,negated_conjecture,
    ( multiply(inverse(sk_c8),sk_c7) = sk_c2
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_31,c_0_126]) ).

cnf(c_0_176,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | sk_c2 = sk_c8
    | sk_c6 = sk_c8 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_77])]) ).

cnf(c_0_177,negated_conjecture,
    ( inverse(sk_c8) = sk_c8
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_114,c_0_167]) ).

cnf(c_0_178,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | inverse(multiply(X1,multiply(X2,identity))) != sk_c6
    | multiply(X1,multiply(X2,sk_c8)) != sk_c6
    | multiply(X3,sk_c7) != sk_c6
    | multiply(X4,sk_c8) != sk_c7
    | inverse(X3) != sk_c7
    | inverse(X4) != sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_28]),c_0_28]) ).

cnf(c_0_179,negated_conjecture,
    ( multiply(sk_c8,multiply(sk_c1,X1)) = X1
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_31,c_0_62]) ).

cnf(c_0_180,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | identity = sk_c6
    | multiply(X1,sk_c7) != sk_c6
    | multiply(X2,sk_c8) != sk_c7
    | inverse(X1) != sk_c7
    | inverse(X2) != sk_c8 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_70]) ).

cnf(c_0_181,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | sk_c6 = sk_c8
    | multiply(X1,sk_c7) != sk_c6
    | multiply(X2,sk_c7) != sk_c6
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X1) != sk_c6
    | inverse(X2) != sk_c7
    | inverse(X3) != sk_c8 ),
    inference(rw,[status(thm)],[c_0_171,c_0_42]) ).

cnf(c_0_182,negated_conjecture,
    ( multiply(inverse(sk_c6),sk_c7) = sk_c6
    | multiply(sk_c3,sk_c8) = sk_c7
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_172,c_0_70]) ).

cnf(c_0_183,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | identity = sk_c7
    | multiply(X1,sk_c7) != sk_c6
    | multiply(X2,sk_c8) != sk_c7
    | inverse(X1) != sk_c7
    | inverse(X2) != sk_c8 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_70]) ).

cnf(c_0_184,negated_conjecture,
    ( sk_c6 = sk_c8
    | sk_c2 = sk_c8 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_94])]) ).

cnf(c_0_185,negated_conjecture,
    ( sk_c6 = sk_c8
    | sk_c2 = sk_c6 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_177]),c_0_77]) ).

cnf(c_0_186,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | multiply(sk_c8,multiply(sk_c1,sk_c8)) != sk_c6
    | multiply(X1,sk_c7) != sk_c6
    | multiply(X2,sk_c8) != sk_c7
    | inverse(X1) != sk_c7
    | inverse(X2) != sk_c8 ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_56]),c_0_180]) ).

cnf(c_0_187,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | sk_c6 = sk_c8
    | multiply(X1,sk_c7) != sk_c6
    | multiply(X2,sk_c8) != sk_c7
    | inverse(X1) != sk_c7
    | inverse(X2) != sk_c8 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_47])]) ).

cnf(c_0_188,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | identity = sk_c7
    | multiply(X1,sk_c8) != sk_c7
    | inverse(sk_c8) != sk_c7
    | inverse(X1) != sk_c8 ),
    inference(spm,[status(thm)],[c_0_183,c_0_174]) ).

cnf(c_0_189,negated_conjecture,
    ( sk_c4 = sk_c7
    | sk_c2 = sk_c7
    | sk_c6 != sk_c8 ),
    inference(spm,[status(thm)],[c_0_57,c_0_138]) ).

cnf(c_0_190,negated_conjecture,
    sk_c6 = sk_c8,
    inference(spm,[status(thm)],[c_0_184,c_0_185]) ).

cnf(c_0_191,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | multiply(X1,sk_c7) != sk_c6
    | multiply(X2,sk_c8) != sk_c7
    | inverse(X1) != sk_c7
    | inverse(X2) != sk_c8 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_179]),c_0_187]) ).

cnf(c_0_192,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | identity = sk_c7
    | multiply(X1,sk_c8) != sk_c7
    | inverse(X1) != sk_c8
    | sk_c7 != sk_c6 ),
    inference(spm,[status(thm)],[c_0_188,c_0_70]) ).

cnf(c_0_193,negated_conjecture,
    ( sk_c2 = sk_c7
    | sk_c4 = sk_c7 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_189,c_0_190])]) ).

cnf(c_0_194,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | multiply(X1,sk_c8) != sk_c7
    | inverse(X1) != sk_c8
    | sk_c7 != sk_c6 ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_30]),c_0_56]),c_0_192]) ).

cnf(c_0_195,negated_conjecture,
    ( sk_c4 = sk_c7
    | sk_c7 = sk_c8 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_193]),c_0_77]),c_0_190]) ).

cnf(c_0_196,negated_conjecture,
    multiply(inverse(sk_c8),sk_c6) = sk_c7,
    inference(spm,[status(thm)],[c_0_31,c_0_77]) ).

cnf(c_0_197,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | sk_c7 != sk_c8
    | identity != sk_c8
    | sk_c7 != sk_c6 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_56]),c_0_30]) ).

cnf(c_0_198,negated_conjecture,
    sk_c7 = sk_c8,
    inference(spm,[status(thm)],[c_0_160,c_0_195]) ).

cnf(c_0_199,negated_conjecture,
    identity = sk_c7,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_190]),c_0_29]) ).

cnf(c_0_200,negated_conjecture,
    multiply(sk_c3,sk_c8) = sk_c8,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_190])]),c_0_198]),c_0_198]),c_0_199]),c_0_198])]) ).

cnf(c_0_201,plain,
    multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
    inference(spm,[status(thm)],[c_0_31,c_0_28]) ).

cnf(c_0_202,negated_conjecture,
    multiply(sk_c3,multiply(sk_c8,X1)) = multiply(sk_c8,X1),
    inference(spm,[status(thm)],[c_0_28,c_0_200]) ).

cnf(c_0_203,negated_conjecture,
    inverse(sk_c8) = sk_c8,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_198]),c_0_198]) ).

cnf(c_0_204,negated_conjecture,
    ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7
    | multiply(X2,sk_c8) != sk_c6
    | multiply(X3,sk_c7) != sk_c6
    | multiply(X4,sk_c8) != sk_c7
    | inverse(sk_c8) != sk_c6
    | inverse(X2) != sk_c6
    | inverse(X3) != sk_c7
    | inverse(X4) != sk_c8
    | inverse(X1) != sk_c8 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_77])]),c_0_94])]) ).

cnf(c_0_205,negated_conjecture,
    multiply(sk_c8,multiply(sk_c8,X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_200]),c_0_203]) ).

cnf(c_0_206,negated_conjecture,
    multiply(sk_c8,sk_c8) = sk_c8,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_190]),c_0_198]) ).

cnf(c_0_207,negated_conjecture,
    ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c8
    | multiply(X2,sk_c8) != sk_c8
    | multiply(X3,sk_c8) != sk_c8
    | multiply(X4,sk_c8) != sk_c8
    | inverse(X2) != sk_c8
    | inverse(X3) != sk_c8
    | inverse(X4) != sk_c8
    | inverse(X1) != sk_c8 ),
    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)],[c_0_204,c_0_190]),c_0_190]),c_0_190]),c_0_190]),c_0_198]),c_0_198]),c_0_198]),c_0_203]),c_0_198])]) ).

cnf(c_0_208,negated_conjecture,
    multiply(sk_c8,X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_205]),c_0_206]),c_0_203]) ).

cnf(c_0_209,plain,
    multiply(X1,sk_c8) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_199]),c_0_198]) ).

cnf(c_0_210,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[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)],[c_0_207,c_0_208]),c_0_209]),c_0_209]),c_0_209]),c_0_209])])])])]),c_0_203])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : GRP308-1 : TPTP v8.2.0. Released v2.5.0.
% 0.12/0.12  % Command    : run_E %s %d THM
% 0.12/0.31  % Computer : n023.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit   : 300
% 0.12/0.31  % WCLimit    : 300
% 0.12/0.31  % DateTime   : Sun May 19 05:50:53 EDT 2024
% 0.12/0.31  % CPUTime    : 
% 0.17/0.42  Running first-order theorem proving
% 0.17/0.42  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.86/0.81  # Version: 3.1.0
% 2.86/0.81  # Preprocessing class: FSMSSMSMSSSNFFN.
% 2.86/0.81  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.86/0.81  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.86/0.81  # Starting new_bool_3 with 300s (1) cores
% 2.86/0.81  # Starting new_bool_1 with 300s (1) cores
% 2.86/0.81  # Starting sh5l with 300s (1) cores
% 2.86/0.81  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 2468 completed with status 0
% 2.86/0.81  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 2.86/0.81  # Preprocessing class: FSMSSMSMSSSNFFN.
% 2.86/0.81  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.86/0.81  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.86/0.81  # No SInE strategy applied
% 2.86/0.81  # Search class: FGHPS-FFMM21-SFFFFFNN
% 2.86/0.81  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.86/0.81  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 2.86/0.81  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 2.86/0.81  # Starting new_bool_3 with 136s (1) cores
% 2.86/0.81  # Starting new_bool_1 with 136s (1) cores
% 2.86/0.81  # Starting sh5l with 136s (1) cores
% 2.86/0.81  # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2472 completed with status 0
% 2.86/0.81  # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 2.86/0.81  # Preprocessing class: FSMSSMSMSSSNFFN.
% 2.86/0.81  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.86/0.81  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 2.86/0.81  # No SInE strategy applied
% 2.86/0.81  # Search class: FGHPS-FFMM21-SFFFFFNN
% 2.86/0.81  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.86/0.81  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 2.86/0.81  # Preprocessing time       : 0.001 s
% 2.86/0.81  # Presaturation interreduction done
% 2.86/0.81  
% 2.86/0.81  # Proof found!
% 2.86/0.81  # SZS status Unsatisfiable
% 2.86/0.81  # SZS output start CNFRefutation
% See solution above
% 2.86/0.81  # Parsed axioms                        : 40
% 2.86/0.81  # Removed by relevancy pruning/SinE    : 0
% 2.86/0.81  # Initial clauses                      : 40
% 2.86/0.81  # Removed in clause preprocessing      : 0
% 2.86/0.81  # Initial clauses in saturation        : 40
% 2.86/0.81  # Processed clauses                    : 7409
% 2.86/0.81  # ...of these trivial                  : 802
% 2.86/0.81  # ...subsumed                          : 4588
% 2.86/0.81  # ...remaining for further processing  : 2019
% 2.86/0.81  # Other redundant clauses eliminated   : 35
% 2.86/0.81  # Clauses deleted for lack of memory   : 0
% 2.86/0.81  # Backward-subsumed                    : 460
% 2.86/0.81  # Backward-rewritten                   : 1468
% 2.86/0.81  # Generated clauses                    : 36824
% 2.86/0.81  # ...of the previous two non-redundant : 35190
% 2.86/0.81  # ...aggressively subsumed             : 0
% 2.86/0.81  # Contextual simplify-reflections      : 132
% 2.86/0.81  # Paramodulations                      : 36781
% 2.86/0.81  # Factorizations                       : 15
% 2.86/0.81  # NegExts                              : 0
% 2.86/0.81  # Equation resolutions                 : 35
% 2.86/0.81  # Disequality decompositions           : 0
% 2.86/0.81  # Total rewrite steps                  : 12923
% 2.86/0.81  # ...of those cached                   : 12483
% 2.86/0.81  # Propositional unsat checks           : 0
% 2.86/0.81  #    Propositional check models        : 0
% 2.86/0.81  #    Propositional check unsatisfiable : 0
% 2.86/0.81  #    Propositional clauses             : 0
% 2.86/0.81  #    Propositional clauses after purity: 0
% 2.86/0.81  #    Propositional unsat core size     : 0
% 2.86/0.81  #    Propositional preprocessing time  : 0.000
% 2.86/0.81  #    Propositional encoding time       : 0.000
% 2.86/0.81  #    Propositional solver time         : 0.000
% 2.86/0.81  #    Success case prop preproc time    : 0.000
% 2.86/0.81  #    Success case prop encoding time   : 0.000
% 2.86/0.81  #    Success case prop solver time     : 0.000
% 2.86/0.81  # Current number of processed clauses  : 47
% 2.86/0.81  #    Positive orientable unit clauses  : 23
% 2.86/0.81  #    Positive unorientable unit clauses: 0
% 2.86/0.81  #    Negative unit clauses             : 0
% 2.86/0.81  #    Non-unit-clauses                  : 24
% 2.86/0.81  # Current number of unprocessed clauses: 4878
% 2.86/0.81  # ...number of literals in the above   : 28324
% 2.86/0.81  # Current number of archived formulas  : 0
% 2.86/0.81  # Current number of archived clauses   : 1968
% 2.86/0.81  # Clause-clause subsumption calls (NU) : 80946
% 2.86/0.81  # Rec. Clause-clause subsumption calls : 26352
% 2.86/0.81  # Non-unit clause-clause subsumptions  : 5122
% 2.86/0.81  # Unit Clause-clause subsumption calls : 1531
% 2.86/0.81  # Rewrite failures with RHS unbound    : 0
% 2.86/0.81  # BW rewrite match attempts            : 99
% 2.86/0.81  # BW rewrite match successes           : 76
% 2.86/0.81  # Condensation attempts                : 0
% 2.86/0.81  # Condensation successes               : 0
% 2.86/0.81  # Termbank termtop insertions          : 402451
% 2.86/0.81  # Search garbage collected termcells   : 32
% 2.86/0.81  
% 2.86/0.81  # -------------------------------------------------
% 2.86/0.81  # User time                : 0.374 s
% 2.86/0.81  # System time              : 0.008 s
% 2.86/0.81  # Total time               : 0.381 s
% 2.86/0.81  # Maximum resident set size: 1676 pages
% 2.86/0.81  
% 2.86/0.81  # -------------------------------------------------
% 2.86/0.81  # User time                : 1.881 s
% 2.86/0.81  # System time              : 0.028 s
% 2.86/0.81  # Total time               : 1.909 s
% 2.86/0.81  # Maximum resident set size: 1764 pages
% 2.86/0.81  % E---3.1 exiting
% 2.86/0.81  % E exiting
%------------------------------------------------------------------------------