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CSE_E---1.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : GRP337-1 : TPTP v9.2.1. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n001.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 : Tue May  5 04:25:37 PM UTC 2026

% Result   : Unsatisfiable 25.29s 15.65s
% Output   : CNFRefutation 25.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   38
%            Number of leaves      :   27
% Syntax   : Number of clauses     :  194 (  34 unt; 139 nHn; 158 RR)
%            Number of literals    :  421 ( 420 equ;  96 neg)
%            Maximal clause size   :   12 (   2 avg)
%            Maximal term depth    :    5 (   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   :   82 (   5 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_27,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | inverse(sk_c4) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).

cnf(prove_this_28,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | inverse(sk_c8) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).

cnf(prove_this_21,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | inverse(sk_c4) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).

cnf(prove_this_22,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | inverse(sk_c8) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).

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

cnf(prove_this_3,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | inverse(sk_c4) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).

cnf(prove_this_15,negated_conjecture,
    ( multiply(sk_c1,sk_c7) = sk_c8
    | inverse(sk_c4) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).

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

cnf(prove_this_19,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | multiply(sk_c7,sk_c6) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).

cnf(prove_this_10,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c8) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).

cnf(prove_this_16,negated_conjecture,
    ( multiply(sk_c1,sk_c7) = sk_c8
    | inverse(sk_c8) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).

cnf(prove_this_25,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | multiply(sk_c7,sk_c6) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).

cnf(prove_this_7,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | multiply(sk_c7,sk_c6) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).

cnf(prove_this_13,negated_conjecture,
    ( multiply(sk_c1,sk_c7) = sk_c8
    | multiply(sk_c7,sk_c6) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).

cnf(prove_this_32,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | multiply(sk_c4,sk_c8) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).

cnf(prove_this_26,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | multiply(sk_c4,sk_c8) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).

cnf(prove_this_2,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | multiply(sk_c4,sk_c8) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).

cnf(prove_this_11,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | multiply(sk_c5,sk_c6) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).

cnf(prove_this_12,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c5) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).

cnf(prove_this_23,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | multiply(sk_c5,sk_c6) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).

cnf(prove_this_30,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | inverse(sk_c5) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).

cnf(prove_this_29,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | multiply(sk_c5,sk_c6) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).

cnf(prove_this_24,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | inverse(sk_c5) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).

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

cnf(c_0_27,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_28,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_29,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_30,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

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

cnf(c_0_32,plain,
    multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_30,c_0_30]) ).

cnf(c_0_33,plain,
    multiply(X1,identity) = X1,
    inference(rw,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_34,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).

cnf(c_0_35,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | inverse(sk_c4) = sk_c8 ),
    prove_this_27 ).

cnf(c_0_36,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | inverse(sk_c8) = sk_c6 ),
    prove_this_28 ).

cnf(c_0_37,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | inverse(sk_c8) = sk_c4 ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_38,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | inverse(sk_c4) = sk_c8 ),
    prove_this_21 ).

cnf(c_0_39,negated_conjecture,
    ( multiply(sk_c3,sk_c2) = identity
    | inverse(sk_c8) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_28,c_0_36]) ).

cnf(c_0_40,negated_conjecture,
    ( multiply(sk_c3,sk_c2) = identity
    | inverse(sk_c8) = sk_c4 ),
    inference(spm,[status(thm)],[c_0_28,c_0_37]) ).

cnf(c_0_41,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | inverse(sk_c8) = sk_c6 ),
    prove_this_22 ).

cnf(c_0_42,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | inverse(sk_c8) = sk_c4 ),
    inference(spm,[status(thm)],[c_0_34,c_0_38]) ).

cnf(c_0_43,negated_conjecture,
    ( multiply(sk_c3,sk_c2) = identity
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_44,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_45,negated_conjecture,
    ( inverse(sk_c3) = sk_c2
    | sk_c4 = sk_c6 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_43]),c_0_33]) ).

cnf(c_0_46,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c4) = sk_c8 ),
    prove_this_9 ).

cnf(c_0_47,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | inverse(sk_c4) = sk_c8 ),
    prove_this_3 ).

cnf(c_0_48,plain,
    multiply(inverse(identity),X1) = X1,
    inference(spm,[status(thm)],[c_0_30,c_0_29]) ).

cnf(c_0_49,negated_conjecture,
    ( multiply(inverse(sk_c2),sk_c7) = sk_c3
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_30,c_0_44]) ).

cnf(c_0_50,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_34,c_0_45]) ).

cnf(c_0_51,negated_conjecture,
    ( multiply(sk_c2,multiply(sk_c3,X1)) = multiply(sk_c7,X1)
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_27,c_0_44]) ).

cnf(c_0_52,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c8) = sk_c4 ),
    inference(spm,[status(thm)],[c_0_34,c_0_46]) ).

cnf(c_0_53,negated_conjecture,
    ( multiply(sk_c1,sk_c7) = sk_c8
    | inverse(sk_c4) = sk_c8 ),
    prove_this_15 ).

cnf(c_0_54,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | inverse(sk_c8) = sk_c6 ),
    prove_this_4 ).

cnf(c_0_55,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | inverse(sk_c8) = sk_c4 ),
    inference(spm,[status(thm)],[c_0_34,c_0_47]) ).

cnf(c_0_56,plain,
    multiply(inverse(inverse(identity)),X1) = X1,
    inference(spm,[status(thm)],[c_0_30,c_0_48]) ).

cnf(c_0_57,negated_conjecture,
    ( multiply(sk_c3,sk_c7) = sk_c3
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_58,negated_conjecture,
    ( multiply(sk_c8,sk_c4) = identity
    | inverse(sk_c2) = sk_c3 ),
    inference(spm,[status(thm)],[c_0_28,c_0_35]) ).

cnf(c_0_59,plain,
    multiply(X1,inverse(X1)) = identity,
    inference(spm,[status(thm)],[c_0_28,c_0_34]) ).

cnf(c_0_60,negated_conjecture,
    ( multiply(sk_c7,sk_c2) = sk_c2
    | sk_c4 = sk_c6 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_43]),c_0_33]) ).

cnf(c_0_61,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | multiply(sk_c7,sk_c6) = sk_c8 ),
    prove_this_19 ).

cnf(c_0_62,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c8) = sk_c6 ),
    prove_this_10 ).

cnf(c_0_63,negated_conjecture,
    ( inverse(sk_c8) = sk_c4
    | inverse(sk_c8) = sk_c1 ),
    inference(spm,[status(thm)],[c_0_34,c_0_52]) ).

cnf(c_0_64,negated_conjecture,
    ( multiply(sk_c1,sk_c7) = sk_c8
    | inverse(sk_c8) = sk_c6 ),
    prove_this_16 ).

cnf(c_0_65,negated_conjecture,
    ( multiply(sk_c1,sk_c7) = sk_c8
    | inverse(sk_c8) = sk_c4 ),
    inference(spm,[status(thm)],[c_0_34,c_0_53]) ).

cnf(c_0_66,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_67,plain,
    inverse(identity) = identity,
    inference(spm,[status(thm)],[c_0_28,c_0_56]) ).

cnf(c_0_68,negated_conjecture,
    ( sk_c4 = sk_c6
    | identity = sk_c7 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_57]),c_0_28]) ).

cnf(c_0_69,plain,
    multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
    inference(spm,[status(thm)],[c_0_30,c_0_27]) ).

cnf(c_0_70,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | multiply(sk_c8,sk_c4) = identity ),
    inference(spm,[status(thm)],[c_0_28,c_0_47]) ).

cnf(c_0_71,negated_conjecture,
    ( multiply(sk_c3,multiply(sk_c2,X1)) = X1
    | multiply(sk_c8,sk_c4) = identity ),
    inference(spm,[status(thm)],[c_0_30,c_0_58]) ).

cnf(c_0_72,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | multiply(sk_c8,sk_c4) = identity ),
    inference(spm,[status(thm)],[c_0_28,c_0_38]) ).

cnf(c_0_73,plain,
    multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
    inference(spm,[status(thm)],[c_0_27,c_0_59]) ).

cnf(c_0_74,negated_conjecture,
    ( multiply(inverse(sk_c7),sk_c2) = sk_c2
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_30,c_0_60]) ).

cnf(c_0_75,negated_conjecture,
    ( multiply(inverse(sk_c2),sk_c7) = sk_c3
    | multiply(sk_c7,sk_c6) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_30,c_0_61]) ).

cnf(c_0_76,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | multiply(sk_c7,sk_c6) = sk_c8 ),
    prove_this_25 ).

cnf(c_0_77,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | inverse(sk_c8) = sk_c1 ),
    inference(spm,[status(thm)],[c_0_34,c_0_62]) ).

cnf(c_0_78,negated_conjecture,
    ( inverse(sk_c8) = sk_c1
    | sk_c4 != sk_c1 ),
    inference(ef,[status(thm)],[c_0_63]) ).

cnf(c_0_79,negated_conjecture,
    ( multiply(sk_c1,sk_c7) = sk_c8
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_80,negated_conjecture,
    ( multiply(inverse(sk_c7),sk_c6) = sk_c8
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_30,c_0_66]) ).

cnf(c_0_81,negated_conjecture,
    ( inverse(sk_c7) = sk_c7
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_82,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | multiply(sk_c7,sk_c6) = sk_c8 ),
    prove_this_7 ).

cnf(c_0_83,negated_conjecture,
    ( multiply(sk_c1,sk_c7) = sk_c8
    | multiply(sk_c7,sk_c6) = sk_c8 ),
    prove_this_13 ).

cnf(c_0_84,negated_conjecture,
    ( multiply(inverse(multiply(X1,sk_c7)),multiply(X1,sk_c6)) = sk_c8
    | multiply(sk_c8,sk_c4) = identity ),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_85,negated_conjecture,
    ( multiply(sk_c8,sk_c4) = identity
    | multiply(sk_c3,sk_c7) = sk_c3 ),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_86,negated_conjecture,
    ( inverse(sk_c7) = identity
    | sk_c4 = sk_c6 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_59]),c_0_33]) ).

cnf(c_0_87,negated_conjecture,
    ( multiply(sk_c7,sk_c6) = sk_c8
    | multiply(sk_c3,sk_c7) = sk_c3 ),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_88,negated_conjecture,
    ( inverse(sk_c8) = sk_c1
    | sk_c4 = sk_c6 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_63]),c_0_78]) ).

cnf(c_0_89,negated_conjecture,
    ( multiply(sk_c1,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_27,c_0_79]) ).

cnf(c_0_90,negated_conjecture,
    ( multiply(sk_c7,sk_c6) = sk_c8
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_80,c_0_81]) ).

cnf(c_0_91,negated_conjecture,
    ( multiply(sk_c8,multiply(sk_c1,X1)) = X1
    | multiply(sk_c7,sk_c6) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_30,c_0_82]) ).

cnf(c_0_92,negated_conjecture,
    ( multiply(sk_c1,multiply(sk_c7,X1)) = multiply(sk_c8,X1)
    | multiply(sk_c7,sk_c6) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_27,c_0_83]) ).

cnf(c_0_93,negated_conjecture,
    ( multiply(sk_c8,sk_c4) = identity
    | sk_c6 = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_30]) ).

cnf(c_0_94,negated_conjecture,
    ( sk_c4 = sk_c6
    | sk_c6 = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_86]),c_0_29]) ).

cnf(c_0_95,negated_conjecture,
    ( multiply(sk_c7,sk_c6) = sk_c8
    | multiply(sk_c7,X1) = X1 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_87]),c_0_30]) ).

cnf(c_0_96,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = identity
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_28,c_0_88]) ).

cnf(c_0_97,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = multiply(sk_c8,sk_c6)
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_89,c_0_90]) ).

cnf(c_0_98,negated_conjecture,
    ( multiply(sk_c8,multiply(sk_c8,X1)) = multiply(sk_c7,X1)
    | multiply(sk_c7,sk_c6) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_99,negated_conjecture,
    ( multiply(sk_c8,sk_c6) = identity
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_93,c_0_94]) ).

cnf(c_0_100,negated_conjecture,
    ( multiply(sk_c7,sk_c6) = sk_c8
    | sk_c6 != sk_c8 ),
    inference(ef,[status(thm)],[c_0_95]) ).

cnf(c_0_101,negated_conjecture,
    ( multiply(sk_c1,multiply(sk_c8,X1)) = X1
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_30,c_0_88]) ).

cnf(c_0_102,negated_conjecture,
    ( multiply(sk_c8,sk_c6) = identity
    | sk_c4 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_96,c_0_97]) ).

cnf(c_0_103,negated_conjecture,
    ( inverse(sk_c8) = sk_c6
    | sk_c1 != sk_c6 ),
    inference(ef,[status(thm)],[c_0_77]) ).

cnf(c_0_104,plain,
    multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_59]),c_0_33]) ).

cnf(c_0_105,negated_conjecture,
    multiply(sk_c7,sk_c6) = sk_c8,
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_33])]),c_0_100]) ).

cnf(c_0_106,negated_conjecture,
    ( sk_c4 = sk_c6
    | sk_c1 = sk_c6 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_33]) ).

cnf(c_0_107,negated_conjecture,
    ( inverse(sk_c6) = sk_c8
    | sk_c1 != sk_c6 ),
    inference(spm,[status(thm)],[c_0_34,c_0_103]) ).

cnf(c_0_108,negated_conjecture,
    ( multiply(sk_c8,sk_c4) = identity
    | inverse(sk_c1) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_28,c_0_46]) ).

cnf(c_0_109,negated_conjecture,
    multiply(inverse(sk_c8),sk_c7) = inverse(sk_c6),
    inference(spm,[status(thm)],[c_0_104,c_0_105]) ).

cnf(c_0_110,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c6) = sk_c8 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_106]),c_0_107]) ).

cnf(c_0_111,negated_conjecture,
    ( multiply(sk_c8,multiply(sk_c1,X1)) = X1
    | multiply(sk_c8,sk_c4) = identity ),
    inference(spm,[status(thm)],[c_0_30,c_0_108]) ).

cnf(c_0_112,negated_conjecture,
    ( multiply(sk_c1,sk_c7) = sk_c8
    | multiply(sk_c8,sk_c4) = identity ),
    inference(spm,[status(thm)],[c_0_28,c_0_53]) ).

cnf(c_0_113,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | sk_c4 != sk_c1 ),
    inference(spm,[status(thm)],[c_0_34,c_0_78]) ).

cnf(c_0_114,negated_conjecture,
    ( multiply(sk_c1,sk_c7) = sk_c8
    | inverse(sk_c6) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_34,c_0_64]) ).

cnf(c_0_115,negated_conjecture,
    ( inverse(sk_c6) = multiply(sk_c1,sk_c7)
    | sk_c4 != sk_c1 ),
    inference(spm,[status(thm)],[c_0_109,c_0_78]) ).

cnf(c_0_116,negated_conjecture,
    multiply(sk_c8,inverse(sk_c6)) = sk_c7,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_109]),c_0_34]) ).

cnf(c_0_117,negated_conjecture,
    ( inverse(sk_c6) = sk_c8
    | inverse(sk_c8) = sk_c1 ),
    inference(spm,[status(thm)],[c_0_34,c_0_110]) ).

cnf(c_0_118,negated_conjecture,
    ( multiply(sk_c8,sk_c4) = identity
    | multiply(sk_c8,sk_c8) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_111,c_0_112]) ).

cnf(c_0_119,negated_conjecture,
    ( multiply(sk_c8,multiply(sk_c1,X1)) = X1
    | sk_c4 != sk_c1 ),
    inference(spm,[status(thm)],[c_0_30,c_0_113]) ).

cnf(c_0_120,negated_conjecture,
    ( multiply(sk_c1,sk_c7) = sk_c8
    | sk_c4 != sk_c1 ),
    inference(spm,[status(thm)],[c_0_114,c_0_115]) ).

cnf(c_0_121,negated_conjecture,
    ( multiply(sk_c8,sk_c8) = sk_c7
    | inverse(sk_c8) = sk_c1 ),
    inference(spm,[status(thm)],[c_0_116,c_0_117]) ).

cnf(c_0_122,negated_conjecture,
    ( multiply(sk_c8,sk_c8) = sk_c7
    | inverse(sk_c8) = sk_c4 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_118]),c_0_33]) ).

cnf(c_0_123,negated_conjecture,
    ( multiply(sk_c8,sk_c8) = sk_c7
    | sk_c4 != sk_c1 ),
    inference(spm,[status(thm)],[c_0_119,c_0_120]) ).

cnf(c_0_124,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | multiply(sk_c4,sk_c8) = sk_c7 ),
    prove_this_32 ).

cnf(c_0_125,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | multiply(sk_c4,sk_c8) = sk_c7 ),
    prove_this_26 ).

cnf(c_0_126,negated_conjecture,
    multiply(sk_c8,sk_c8) = sk_c7,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123]) ).

cnf(c_0_127,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | multiply(sk_c4,sk_c8) = sk_c7 ),
    prove_this_2 ).

cnf(c_0_128,negated_conjecture,
    ( multiply(sk_c4,multiply(sk_c8,X1)) = multiply(sk_c7,X1)
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_27,c_0_124]) ).

cnf(c_0_129,negated_conjecture,
    multiply(inverse(sk_c7),sk_c8) = sk_c6,
    inference(spm,[status(thm)],[c_0_30,c_0_105]) ).

cnf(c_0_130,negated_conjecture,
    ( multiply(sk_c4,sk_c8) = sk_c7
    | multiply(sk_c3,sk_c2) = identity ),
    inference(spm,[status(thm)],[c_0_28,c_0_125]) ).

cnf(c_0_131,negated_conjecture,
    inverse(sk_c6) = sk_c8,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_126]),c_0_109]) ).

cnf(c_0_132,negated_conjecture,
    ( multiply(sk_c4,multiply(sk_c8,X1)) = multiply(sk_c7,X1)
    | multiply(sk_c7,sk_c8) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_27,c_0_127]) ).

cnf(c_0_133,negated_conjecture,
    ( multiply(sk_c7,inverse(sk_c8)) = sk_c4
    | multiply(sk_c3,sk_c8) = sk_c7 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_59]),c_0_33]) ).

cnf(c_0_134,negated_conjecture,
    inverse(sk_c8) = sk_c6,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_126]),c_0_129]) ).

cnf(c_0_135,negated_conjecture,
    ( multiply(sk_c4,multiply(sk_c8,X1)) = multiply(sk_c7,X1)
    | multiply(sk_c3,sk_c2) = identity ),
    inference(spm,[status(thm)],[c_0_27,c_0_130]) ).

cnf(c_0_136,negated_conjecture,
    multiply(sk_c8,sk_c6) = identity,
    inference(spm,[status(thm)],[c_0_28,c_0_131]) ).

cnf(c_0_137,negated_conjecture,
    ( multiply(sk_c7,inverse(sk_c8)) = sk_c4
    | multiply(sk_c7,sk_c8) = sk_c6 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_59]),c_0_33]) ).

cnf(c_0_138,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | multiply(sk_c5,sk_c6) = sk_c7 ),
    prove_this_11 ).

cnf(c_0_139,negated_conjecture,
    ( multiply(sk_c3,sk_c8) = sk_c7
    | sk_c4 = sk_c8 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134]),c_0_105]) ).

cnf(c_0_140,negated_conjecture,
    ( multiply(sk_c3,sk_c2) = identity
    | sk_c4 = sk_c8 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_33]),c_0_105]) ).

cnf(c_0_141,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c6
    | sk_c4 = sk_c8 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_134]),c_0_105]) ).

cnf(c_0_142,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | inverse(sk_c5) = sk_c6 ),
    prove_this_12 ).

cnf(c_0_143,negated_conjecture,
    ( multiply(sk_c5,sk_c6) = sk_c7
    | inverse(sk_c8) = sk_c1 ),
    inference(spm,[status(thm)],[c_0_34,c_0_138]) ).

cnf(c_0_144,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | multiply(sk_c5,sk_c6) = sk_c7 ),
    prove_this_23 ).

cnf(c_0_145,negated_conjecture,
    ( multiply(inverse(sk_c3),sk_c7) = sk_c8
    | sk_c4 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_30,c_0_139]) ).

cnf(c_0_146,negated_conjecture,
    ( inverse(sk_c3) = sk_c2
    | sk_c4 = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_140]),c_0_33]) ).

cnf(c_0_147,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | inverse(sk_c5) = sk_c6 ),
    prove_this_30 ).

cnf(c_0_148,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | multiply(sk_c5,sk_c6) = sk_c7 ),
    prove_this_29 ).

cnf(c_0_149,negated_conjecture,
    ( multiply(sk_c1,multiply(sk_c8,X1)) = X1
    | sk_c4 != sk_c1 ),
    inference(spm,[status(thm)],[c_0_30,c_0_78]) ).

cnf(c_0_150,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | sk_c4 = sk_c8 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_141]),c_0_131]),c_0_134]) ).

cnf(c_0_151,negated_conjecture,
    ( multiply(sk_c6,multiply(sk_c5,X1)) = X1
    | inverse(sk_c1) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_30,c_0_142]) ).

cnf(c_0_152,negated_conjecture,
    ( multiply(sk_c5,sk_c6) = sk_c7
    | sk_c1 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_143,c_0_134]) ).

cnf(c_0_153,negated_conjecture,
    multiply(sk_c6,sk_c7) = sk_c8,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_131]),c_0_134]) ).

cnf(c_0_154,negated_conjecture,
    ( multiply(inverse(sk_c5),sk_c7) = sk_c6
    | multiply(sk_c2,sk_c3) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_30,c_0_144]) ).

cnf(c_0_155,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | inverse(sk_c5) = sk_c6 ),
    prove_this_24 ).

cnf(c_0_156,negated_conjecture,
    ( multiply(sk_c2,sk_c7) = sk_c8
    | sk_c4 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_145,c_0_146]) ).

cnf(c_0_157,negated_conjecture,
    ( multiply(sk_c6,multiply(sk_c5,X1)) = X1
    | inverse(sk_c2) = sk_c3 ),
    inference(spm,[status(thm)],[c_0_30,c_0_147]) ).

cnf(c_0_158,negated_conjecture,
    ( multiply(sk_c5,sk_c6) = sk_c7
    | multiply(sk_c3,sk_c2) = identity ),
    inference(spm,[status(thm)],[c_0_28,c_0_148]) ).

cnf(c_0_159,negated_conjecture,
    ( multiply(sk_c1,sk_c6) = sk_c7
    | sk_c4 = sk_c8
    | sk_c4 != sk_c1 ),
    inference(spm,[status(thm)],[c_0_149,c_0_150]) ).

cnf(c_0_160,negated_conjecture,
    ( inverse(sk_c1) = sk_c8
    | sk_c1 = sk_c6
    | sk_c6 = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]) ).

cnf(c_0_161,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | multiply(sk_c6,sk_c7) = sk_c6 ),
    inference(spm,[status(thm)],[c_0_154,c_0_155]) ).

cnf(c_0_162,negated_conjecture,
    ( multiply(sk_c2,sk_c8) = identity
    | sk_c4 = sk_c8 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_156]),c_0_134]),c_0_105]) ).

cnf(c_0_163,negated_conjecture,
    ( multiply(sk_c3,sk_c2) = identity
    | inverse(sk_c2) = sk_c3
    | sk_c6 = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_153]) ).

cnf(c_0_164,negated_conjecture,
    ( multiply(sk_c1,sk_c6) = sk_c7
    | sk_c6 = sk_c8
    | sk_c1 != sk_c6 ),
    inference(spm,[status(thm)],[c_0_159,c_0_94]) ).

cnf(c_0_165,negated_conjecture,
    ( sk_c6 = sk_c8
    | sk_c1 = sk_c6 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_160]),c_0_134])]) ).

cnf(c_0_166,negated_conjecture,
    ( multiply(sk_c2,sk_c3) = sk_c7
    | sk_c6 = sk_c8 ),
    inference(rw,[status(thm)],[c_0_161,c_0_153]) ).

cnf(c_0_167,negated_conjecture,
    ( sk_c4 = sk_c8
    | sk_c2 = sk_c6 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_162]),c_0_67]),c_0_29]),c_0_134]) ).

cnf(c_0_168,negated_conjecture,
    ( multiply(sk_c7,sk_c8) != sk_c6
    | inverse(X1) != sk_c8
    | multiply(X1,sk_c7) != sk_c8
    | multiply(X2,X3) != sk_c7
    | inverse(X2) != X3
    | multiply(X3,sk_c8) != sk_c7
    | multiply(sk_c7,sk_c6) != sk_c8
    | multiply(X4,sk_c8) != sk_c7
    | inverse(X4) != sk_c8
    | inverse(sk_c8) != sk_c6
    | multiply(X5,sk_c6) != sk_c7
    | inverse(X5) != sk_c6 ),
    prove_this_37 ).

cnf(c_0_169,negated_conjecture,
    ( multiply(sk_c3,sk_c2) = identity
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_28,c_0_163]) ).

cnf(c_0_170,negated_conjecture,
    ( multiply(sk_c8,multiply(sk_c6,X1)) = X1
    | sk_c1 != sk_c6 ),
    inference(spm,[status(thm)],[c_0_30,c_0_107]) ).

cnf(c_0_171,negated_conjecture,
    ( multiply(sk_c6,sk_c6) = sk_c7
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_164,c_0_165]) ).

cnf(c_0_172,negated_conjecture,
    ( multiply(inverse(sk_c2),sk_c7) = sk_c3
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_30,c_0_166]) ).

cnf(c_0_173,negated_conjecture,
    ( sk_c2 = sk_c6
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_94,c_0_167]) ).

cnf(c_0_174,negated_conjecture,
    ( multiply(inverse(X1),sk_c8) != sk_c7
    | multiply(sk_c7,sk_c8) != sk_c6
    | multiply(sk_c7,sk_c6) != sk_c8
    | multiply(X1,inverse(X1)) != sk_c7
    | multiply(X2,sk_c6) != sk_c7
    | multiply(X3,sk_c8) != sk_c7
    | multiply(X4,sk_c7) != sk_c8
    | inverse(sk_c8) != sk_c6
    | inverse(X2) != sk_c6
    | inverse(X3) != sk_c8
    | inverse(X4) != sk_c8 ),
    inference(er,[status(thm)],[c_0_168]) ).

cnf(c_0_175,negated_conjecture,
    ( inverse(sk_c2) = sk_c3
    | sk_c6 = sk_c8 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_169]),c_0_67]),c_0_29]) ).

cnf(c_0_176,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c6
    | sk_c6 = sk_c8 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_165]) ).

cnf(c_0_177,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c3
    | sk_c6 = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_131]) ).

cnf(c_0_178,negated_conjecture,
    ( multiply(inverse(X1),sk_c8) != sk_c7
    | multiply(sk_c7,sk_c8) != sk_c6
    | multiply(sk_c7,sk_c6) != sk_c8
    | multiply(X2,sk_c6) != sk_c7
    | multiply(X3,sk_c8) != sk_c7
    | multiply(X4,sk_c7) != sk_c8
    | inverse(sk_c8) != sk_c6
    | inverse(X2) != sk_c6
    | inverse(X3) != sk_c8
    | inverse(X4) != sk_c8
    | identity != sk_c7 ),
    inference(rw,[status(thm)],[c_0_174,c_0_59]) ).

cnf(c_0_179,negated_conjecture,
    ( multiply(sk_c3,sk_c7) = sk_c3
    | sk_c6 = sk_c8 ),
    inference(spm,[status(thm)],[c_0_172,c_0_175]) ).

cnf(c_0_180,negated_conjecture,
    ( sk_c6 = sk_c8
    | sk_c3 = sk_c6 ),
    inference(spm,[status(thm)],[c_0_176,c_0_177]) ).

cnf(c_0_181,negated_conjecture,
    ( multiply(inverse(X1),sk_c8) != sk_c7
    | multiply(sk_c7,sk_c8) != sk_c6
    | multiply(X2,sk_c6) != sk_c7
    | multiply(X3,sk_c8) != sk_c7
    | multiply(X4,sk_c7) != sk_c8
    | inverse(sk_c8) != sk_c6
    | inverse(X2) != sk_c6
    | inverse(X3) != sk_c8
    | inverse(X4) != sk_c8
    | identity != sk_c7 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_178,c_0_105])]) ).

cnf(c_0_182,negated_conjecture,
    sk_c6 = sk_c8,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_153])]) ).

cnf(c_0_183,negated_conjecture,
    multiply(sk_c6,sk_c8) = identity,
    inference(spm,[status(thm)],[c_0_59,c_0_131]) ).

cnf(c_0_184,negated_conjecture,
    ( multiply(inverse(X1),sk_c8) != sk_c7
    | multiply(sk_c7,sk_c8) != sk_c6
    | multiply(X2,sk_c6) != sk_c7
    | multiply(X3,sk_c8) != sk_c7
    | multiply(X4,sk_c7) != sk_c8
    | inverse(X2) != sk_c6
    | inverse(X3) != sk_c8
    | inverse(X4) != sk_c8
    | identity != sk_c7 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_134])]) ).

cnf(c_0_185,negated_conjecture,
    multiply(sk_c7,sk_c8) = sk_c8,
    inference(rw,[status(thm)],[c_0_105,c_0_182]) ).

cnf(c_0_186,negated_conjecture,
    identity = sk_c7,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_183,c_0_182]),c_0_126]) ).

cnf(c_0_187,negated_conjecture,
    ( multiply(inverse(X1),sk_c8) != sk_c7
    | multiply(X2,sk_c8) != sk_c7
    | multiply(X3,sk_c8) != sk_c7
    | multiply(X4,sk_c7) != sk_c8
    | inverse(X2) != sk_c8
    | inverse(X3) != sk_c8
    | inverse(X4) != 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)],[c_0_184,c_0_182]),c_0_182]),c_0_182]),c_0_185]),c_0_186])]) ).

cnf(c_0_188,plain,
    multiply(X1,sk_c7) = X1,
    inference(rw,[status(thm)],[c_0_33,c_0_186]) ).

cnf(c_0_189,negated_conjecture,
    ( multiply(inverse(X1),sk_c8) != sk_c7
    | multiply(X2,sk_c8) != sk_c7
    | multiply(X3,sk_c8) != sk_c7
    | inverse(X2) != sk_c8
    | inverse(X3) != sk_c8 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_187,c_0_188])]),c_0_134]),c_0_182])]) ).

cnf(c_0_190,negated_conjecture,
    inverse(sk_c8) = sk_c8,
    inference(rw,[status(thm)],[c_0_134,c_0_182]) ).

cnf(c_0_191,negated_conjecture,
    ( multiply(X1,sk_c8) != sk_c7
    | multiply(X2,sk_c8) != sk_c7
    | inverse(X1) != sk_c8
    | inverse(X2) != sk_c8 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_126])]) ).

cnf(c_0_192,negated_conjecture,
    ( multiply(X1,sk_c8) != sk_c7
    | inverse(X1) != sk_c8 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_126]),c_0_134]),c_0_182])]) ).

cnf(c_0_193,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_190]),c_0_126])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP337-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33  % Computer : n001.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Mon May  4 18:33:03 EDT 2026
% 0.14/0.33  % CPUTime    : 
% 0.14/0.34  % start to proof: theBenchmark
% 25.29/15.65  % Version  : CSE_E---1.7
% 25.29/15.65  % Problem  : theBenchmark.p
% 25.29/15.65  % SZS status Unsatisfiable for theBenchmark.p
% 25.29/15.65  % SZS output start CNFRefutation
% See solution above
% 25.39/15.76  % Total time : 11.393s
%------------------------------------------------------------------------------