TSTP Solution File: GRP219-1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : GRP219-1 : 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 20:54:52 EDT 2024

% Result   : Unsatisfiable 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   96 (  21 unt;  67 nHn;  79 RR)
%            Number of literals    :  240 ( 239 equ;  75 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    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   64 (   4 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_6,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c9
    | multiply(sk_c6,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).

cnf(prove_this_2,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c6,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).

cnf(prove_this_5,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c9
    | inverse(sk_c6) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).

cnf(prove_this_23,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | multiply(sk_c7,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).

cnf(prove_this_1,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | inverse(sk_c6) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).

cnf(prove_this_24,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | inverse(sk_c7) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).

cnf(prove_this_33,negated_conjecture,
    ( inverse(X1) != sk_c9
    | multiply(X1,sk_c8) != sk_c9
    | multiply(X2,X3) != sk_c8
    | inverse(X2) != X3
    | multiply(X3,sk_c9) != sk_c8
    | multiply(sk_c9,X4) != sk_c8
    | multiply(X5,sk_c9) != X4
    | inverse(X5) != sk_c9
    | inverse(X6) != sk_c9
    | multiply(X6,sk_c8) != sk_c9
    | multiply(X7,sk_c8) != sk_c9
    | inverse(X7) != sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).

cnf(prove_this_22,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | multiply(sk_c6,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).

cnf(prove_this_21,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | inverse(sk_c6) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).

cnf(prove_this_27,negated_conjecture,
    ( multiply(sk_c4,sk_c9) = sk_c5
    | multiply(sk_c7,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).

cnf(prove_this_31,negated_conjecture,
    ( inverse(sk_c4) = sk_c9
    | multiply(sk_c7,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).

cnf(prove_this_28,negated_conjecture,
    ( multiply(sk_c4,sk_c9) = sk_c5
    | inverse(sk_c7) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).

cnf(prove_this_32,negated_conjecture,
    ( inverse(sk_c4) = sk_c9
    | inverse(sk_c7) = sk_c8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).

cnf(c_0_16,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_17,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_18,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_19,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

cnf(c_0_20,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c9
    | multiply(sk_c6,sk_c8) = sk_c9 ),
    prove_this_6 ).

cnf(c_0_21,negated_conjecture,
    ( multiply(inverse(sk_c1),sk_c9) = sk_c8
    | multiply(sk_c6,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_22,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c6,sk_c8) = sk_c9 ),
    prove_this_2 ).

cnf(c_0_23,negated_conjecture,
    ( multiply(sk_c6,sk_c8) = sk_c9
    | multiply(sk_c9,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_24,negated_conjecture,
    ( multiply(inverse(sk_c6),sk_c9) = sk_c8
    | multiply(sk_c9,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_19,c_0_23]) ).

cnf(c_0_25,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c9
    | inverse(sk_c6) = sk_c9 ),
    prove_this_5 ).

cnf(c_0_26,negated_conjecture,
    ( multiply(sk_c1,sk_c8) = sk_c9
    | multiply(sk_c9,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_27,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | multiply(sk_c7,sk_c8) = sk_c9 ),
    prove_this_23 ).

cnf(c_0_28,negated_conjecture,
    ( multiply(inverse(sk_c1),sk_c9) = sk_c8
    | multiply(sk_c9,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_19,c_0_26]) ).

cnf(c_0_29,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | inverse(sk_c6) = sk_c9 ),
    prove_this_1 ).

cnf(c_0_30,negated_conjecture,
    ( multiply(inverse(sk_c7),sk_c9) = sk_c8
    | multiply(sk_c9,sk_c5) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_19,c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | inverse(sk_c7) = sk_c8 ),
    prove_this_24 ).

cnf(c_0_32,negated_conjecture,
    ( multiply(sk_c9,sk_c9) = sk_c8
    | inverse(sk_c6) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,negated_conjecture,
    ( multiply(sk_c7,multiply(sk_c8,X1)) = multiply(sk_c9,X1)
    | multiply(sk_c9,sk_c5) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_16,c_0_27]) ).

cnf(c_0_34,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | multiply(sk_c8,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    multiply(sk_c9,sk_c9) = sk_c8,
    inference(spm,[status(thm)],[c_0_24,c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | multiply(sk_c7,sk_c8) = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).

cnf(c_0_37,negated_conjecture,
    ( multiply(inverse(sk_c7),sk_c8) = sk_c8
    | multiply(sk_c9,sk_c5) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_19,c_0_36]) ).

cnf(c_0_38,negated_conjecture,
    ( inverse(X1) != sk_c9
    | multiply(X1,sk_c8) != sk_c9
    | multiply(X2,X3) != sk_c8
    | inverse(X2) != X3
    | multiply(X3,sk_c9) != sk_c8
    | multiply(sk_c9,X4) != sk_c8
    | multiply(X5,sk_c9) != X4
    | inverse(X5) != sk_c9
    | inverse(X6) != sk_c9
    | multiply(X6,sk_c8) != sk_c9
    | multiply(X7,sk_c8) != sk_c9
    | inverse(X7) != sk_c8 ),
    inference(fof_simplification,[status(thm)],[prove_this_33]) ).

cnf(c_0_39,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | multiply(sk_c8,sk_c8) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_37,c_0_31]) ).

cnf(c_0_40,negated_conjecture,
    ( inverse(X1) != sk_c9
    | multiply(X1,sk_c8) != sk_c9
    | multiply(X2,X3) != sk_c8
    | inverse(X2) != X3
    | multiply(X3,sk_c9) != sk_c8
    | multiply(sk_c9,X4) != sk_c8
    | multiply(X5,sk_c9) != X4
    | inverse(X5) != sk_c9
    | inverse(X6) != sk_c9
    | multiply(X6,sk_c8) != sk_c9
    | multiply(X7,sk_c8) != sk_c9
    | inverse(X7) != sk_c8 ),
    c_0_38 ).

cnf(c_0_41,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | identity = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_39]),c_0_17]) ).

cnf(c_0_42,negated_conjecture,
    multiply(inverse(sk_c9),sk_c8) = sk_c9,
    inference(spm,[status(thm)],[c_0_19,c_0_35]) ).

cnf(c_0_43,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | identity = sk_c9 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_34]),c_0_17]) ).

cnf(c_0_44,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(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_45,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | multiply(sk_c6,sk_c8) = sk_c9 ),
    prove_this_22 ).

cnf(c_0_46,negated_conjecture,
    ( identity = sk_c8
    | sk_c5 = sk_c9 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_41]),c_0_42]) ).

cnf(c_0_47,negated_conjecture,
    ( identity = sk_c9
    | sk_c5 = sk_c9 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_43]),c_0_42]) ).

cnf(c_0_48,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = 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
    | inverse(X3) != sk_c9
    | inverse(X1) != sk_c9
    | inverse(X4) != sk_c9 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_31]),c_0_27]) ).

cnf(c_0_49,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | inverse(sk_c6) = sk_c9 ),
    prove_this_21 ).

cnf(c_0_50,negated_conjecture,
    ( multiply(sk_c6,multiply(sk_c8,X1)) = multiply(sk_c9,X1)
    | multiply(sk_c9,sk_c5) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_16,c_0_45]) ).

cnf(c_0_51,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | multiply(sk_c8,sk_c7) = identity ),
    inference(spm,[status(thm)],[c_0_17,c_0_31]) ).

cnf(c_0_52,negated_conjecture,
    ( multiply(sk_c8,X1) = X1
    | sk_c5 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_18,c_0_46]) ).

cnf(c_0_53,negated_conjecture,
    ( multiply(sk_c4,sk_c9) = sk_c5
    | multiply(sk_c7,sk_c8) = sk_c9 ),
    prove_this_27 ).

cnf(c_0_54,negated_conjecture,
    ( multiply(sk_c9,X1) = X1
    | sk_c5 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_18,c_0_47]) ).

cnf(c_0_55,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = 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
    | inverse(X1) != sk_c9
    | inverse(X3) != sk_c9 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_45]) ).

cnf(c_0_56,plain,
    multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_19,c_0_19]) ).

cnf(c_0_57,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | multiply(sk_c6,sk_c8) = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_34]),c_0_35]) ).

cnf(c_0_58,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | sk_c5 = sk_c9
    | identity = sk_c7 ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_59,negated_conjecture,
    ( multiply(inverse(sk_c4),sk_c5) = sk_c9
    | multiply(sk_c7,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_19,c_0_53]) ).

cnf(c_0_60,negated_conjecture,
    ( sk_c5 = sk_c9
    | sk_c8 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_35,c_0_54]) ).

cnf(c_0_61,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | multiply(sk_c9,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
    | inverse(X2) != sk_c9
    | sk_c8 != sk_c9 ),
    inference(spm,[status(thm)],[c_0_55,c_0_31]) ).

cnf(c_0_62,plain,
    multiply(X1,inverse(X1)) = identity,
    inference(spm,[status(thm)],[c_0_17,c_0_56]) ).

cnf(c_0_63,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | sk_c8 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_45,c_0_57]) ).

cnf(c_0_64,negated_conjecture,
    ( identity = sk_c7
    | sk_c5 = sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_58]),c_0_42])]) ).

cnf(c_0_65,negated_conjecture,
    ( multiply(inverse(sk_c4),sk_c9) = sk_c9
    | multiply(sk_c7,sk_c8) = sk_c9
    | sk_c8 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_66,negated_conjecture,
    ( inverse(sk_c4) = sk_c9
    | multiply(sk_c7,sk_c8) = sk_c9 ),
    prove_this_31 ).

cnf(c_0_67,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | multiply(sk_c9,multiply(sk_c7,sk_c9)) != sk_c8
    | multiply(inverse(X1),sk_c9) != sk_c8
    | multiply(X2,sk_c8) != sk_c9
    | inverse(X2) != sk_c9 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_41]) ).

cnf(c_0_68,negated_conjecture,
    ( multiply(sk_c7,X1) = X1
    | sk_c5 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_18,c_0_64]) ).

cnf(c_0_69,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = sk_c9
    | sk_c8 = sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_35])]) ).

cnf(c_0_70,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | sk_c5 = sk_c9
    | multiply(inverse(X1),sk_c9) != sk_c8
    | multiply(X2,sk_c8) != sk_c9
    | inverse(X2) != sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_35])]) ).

cnf(c_0_71,plain,
    inverse(identity) = identity,
    inference(spm,[status(thm)],[c_0_18,c_0_62]) ).

cnf(c_0_72,negated_conjecture,
    ( multiply(inverse(sk_c7),sk_c9) = sk_c8
    | sk_c8 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_19,c_0_69]) ).

cnf(c_0_73,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | sk_c5 = sk_c9
    | multiply(inverse(X1),sk_c9) != sk_c8 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_18]),c_0_47]),c_0_60]) ).

cnf(c_0_74,negated_conjecture,
    ( inverse(sk_c7) = identity
    | sk_c5 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_68,c_0_62]) ).

cnf(c_0_75,negated_conjecture,
    ( multiply(inverse(inverse(sk_c7)),sk_c8) = sk_c9
    | sk_c8 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_19,c_0_72]) ).

cnf(c_0_76,negated_conjecture,
    ( multiply(sk_c4,sk_c9) = sk_c5
    | inverse(sk_c7) = sk_c8 ),
    prove_this_28 ).

cnf(c_0_77,negated_conjecture,
    ( multiply(sk_c9,sk_c5) = sk_c8
    | sk_c5 = sk_c9 ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_18]),c_0_60]) ).

cnf(c_0_78,negated_conjecture,
    ( multiply(sk_c4,sk_c9) = sk_c5
    | sk_c8 = sk_c9
    | identity = sk_c9 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_17]) ).

cnf(c_0_79,negated_conjecture,
    sk_c5 = sk_c9,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_77]),c_0_42])]) ).

cnf(c_0_80,negated_conjecture,
    ( multiply(sk_c4,sk_c9) = sk_c9
    | identity = sk_c9
    | sk_c8 = sk_c9 ),
    inference(rw,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_81,negated_conjecture,
    ( multiply(inverse(sk_c4),sk_c9) = sk_c9
    | sk_c8 = sk_c9
    | identity = sk_c9 ),
    inference(spm,[status(thm)],[c_0_19,c_0_80]) ).

cnf(c_0_82,negated_conjecture,
    ( inverse(sk_c4) = sk_c9
    | inverse(sk_c7) = sk_c8 ),
    prove_this_32 ).

cnf(c_0_83,negated_conjecture,
    ( inverse(sk_c7) = sk_c8
    | identity = sk_c9
    | sk_c8 = sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_35])]) ).

cnf(c_0_84,negated_conjecture,
    ( multiply(sk_c7,sk_c8) = identity
    | sk_c8 = sk_c9
    | identity = sk_c9 ),
    inference(spm,[status(thm)],[c_0_62,c_0_83]) ).

cnf(c_0_85,negated_conjecture,
    ( sk_c8 = sk_c9
    | identity = sk_c9 ),
    inference(spm,[status(thm)],[c_0_69,c_0_84]) ).

cnf(c_0_86,negated_conjecture,
    ( inverse(sk_c9) = sk_c9
    | sk_c8 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_71,c_0_85]) ).

cnf(c_0_87,negated_conjecture,
    ( sk_c8 = sk_c9
    | identity = sk_c8 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_86]),c_0_35]) ).

cnf(c_0_88,negated_conjecture,
    sk_c8 = sk_c9,
    inference(spm,[status(thm)],[c_0_85,c_0_87]) ).

cnf(c_0_89,negated_conjecture,
    identity = sk_c9,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_88]),c_0_17]) ).

cnf(c_0_90,plain,
    multiply(inverse(X1),X1) = sk_c9,
    inference(rw,[status(thm)],[c_0_17,c_0_89]) ).

cnf(c_0_91,plain,
    multiply(sk_c9,X1) = X1,
    inference(rw,[status(thm)],[c_0_18,c_0_89]) ).

cnf(c_0_92,plain,
    multiply(X1,sk_c9) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_90]),c_0_56]) ).

cnf(c_0_93,plain,
    inverse(sk_c9) = sk_c9,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_89]),c_0_89]) ).

cnf(c_0_94,negated_conjecture,
    inverse(X1) != sk_c9,
    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(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(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_62]),c_0_91]),c_0_92]),c_0_88]),c_0_92]),c_0_88]),c_0_89]),c_0_88]),c_0_88]),c_0_92]),c_0_88]),c_0_92]),c_0_88]),c_0_92]),c_0_88])])])])])]),c_0_93])]) ).

cnf(c_0_95,plain,
    $false,
    inference(sr,[status(thm)],[c_0_93,c_0_94]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP219-1 : TPTP v8.2.0. Released v2.5.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 06:00:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.51  Running first-order model finding
% 0.20/0.51  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.59  # Version: 3.1.0
% 0.20/0.59  # Preprocessing class: FSMSSMSMSSSNFFN.
% 0.20/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.20/0.59  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.59  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.59  # Starting sh5l with 300s (1) cores
% 0.20/0.59  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 26475 completed with status 0
% 0.20/0.59  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.20/0.59  # Preprocessing class: FSMSSMSMSSSNFFN.
% 0.20/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.20/0.59  # No SInE strategy applied
% 0.20/0.59  # Search class: FGHPS-FFMM21-SFFFFFNN
% 0.20/0.59  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.59  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 0.20/0.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.20/0.59  # Starting new_bool_3 with 136s (1) cores
% 0.20/0.59  # Starting new_bool_1 with 136s (1) cores
% 0.20/0.59  # Starting sh5l with 136s (1) cores
% 0.20/0.59  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 26480 completed with status 0
% 0.20/0.59  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.20/0.59  # Preprocessing class: FSMSSMSMSSSNFFN.
% 0.20/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.20/0.59  # No SInE strategy applied
% 0.20/0.59  # Search class: FGHPS-FFMM21-SFFFFFNN
% 0.20/0.59  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.59  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 0.20/0.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.20/0.59  # Preprocessing time       : 0.001 s
% 0.20/0.59  # Presaturation interreduction done
% 0.20/0.59  
% 0.20/0.59  # Proof found!
% 0.20/0.59  # SZS status Unsatisfiable
% 0.20/0.59  # SZS output start CNFRefutation
% See solution above
% 0.20/0.59  # Parsed axioms                        : 36
% 0.20/0.59  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.59  # Initial clauses                      : 36
% 0.20/0.59  # Removed in clause preprocessing      : 0
% 0.20/0.59  # Initial clauses in saturation        : 36
% 0.20/0.59  # Processed clauses                    : 888
% 0.20/0.59  # ...of these trivial                  : 83
% 0.20/0.59  # ...subsumed                          : 367
% 0.20/0.59  # ...remaining for further processing  : 438
% 0.20/0.59  # Other redundant clauses eliminated   : 16
% 0.20/0.59  # Clauses deleted for lack of memory   : 0
% 0.20/0.59  # Backward-subsumed                    : 61
% 0.20/0.59  # Backward-rewritten                   : 321
% 0.20/0.59  # Generated clauses                    : 2323
% 0.20/0.59  # ...of the previous two non-redundant : 2310
% 0.20/0.59  # ...aggressively subsumed             : 0
% 0.20/0.59  # Contextual simplify-reflections      : 38
% 0.20/0.59  # Paramodulations                      : 2312
% 0.20/0.59  # Factorizations                       : 3
% 0.20/0.59  # NegExts                              : 0
% 0.20/0.59  # Equation resolutions                 : 16
% 0.20/0.59  # Disequality decompositions           : 0
% 0.20/0.59  # Total rewrite steps                  : 1475
% 0.20/0.59  # ...of those cached                   : 1392
% 0.20/0.59  # Propositional unsat checks           : 0
% 0.20/0.59  #    Propositional check models        : 0
% 0.20/0.59  #    Propositional check unsatisfiable : 0
% 0.20/0.59  #    Propositional clauses             : 0
% 0.20/0.59  #    Propositional clauses after purity: 0
% 0.20/0.59  #    Propositional unsat core size     : 0
% 0.20/0.59  #    Propositional preprocessing time  : 0.000
% 0.20/0.59  #    Propositional encoding time       : 0.000
% 0.20/0.59  #    Propositional solver time         : 0.000
% 0.20/0.59  #    Success case prop preproc time    : 0.000
% 0.20/0.59  #    Success case prop encoding time   : 0.000
% 0.20/0.59  #    Success case prop solver time     : 0.000
% 0.20/0.59  # Current number of processed clauses  : 14
% 0.20/0.59  #    Positive orientable unit clauses  : 13
% 0.20/0.59  #    Positive unorientable unit clauses: 0
% 0.20/0.59  #    Negative unit clauses             : 1
% 0.20/0.59  #    Non-unit-clauses                  : 0
% 0.20/0.59  # Current number of unprocessed clauses: 1071
% 0.20/0.59  # ...number of literals in the above   : 3269
% 0.20/0.59  # Current number of archived formulas  : 0
% 0.20/0.59  # Current number of archived clauses   : 419
% 0.20/0.59  # Clause-clause subsumption calls (NU) : 4815
% 0.20/0.59  # Rec. Clause-clause subsumption calls : 2250
% 0.20/0.59  # Non-unit clause-clause subsumptions  : 460
% 0.20/0.59  # Unit Clause-clause subsumption calls : 251
% 0.20/0.59  # Rewrite failures with RHS unbound    : 0
% 0.20/0.59  # BW rewrite match attempts            : 29
% 0.20/0.59  # BW rewrite match successes           : 26
% 0.20/0.59  # Condensation attempts                : 0
% 0.20/0.59  # Condensation successes               : 0
% 0.20/0.59  # Termbank termtop insertions          : 36763
% 0.20/0.59  # Search garbage collected termcells   : 35
% 0.20/0.59  
% 0.20/0.59  # -------------------------------------------------
% 0.20/0.59  # User time                : 0.062 s
% 0.20/0.59  # System time              : 0.004 s
% 0.20/0.59  # Total time               : 0.066 s
% 0.20/0.59  # Maximum resident set size: 1660 pages
% 0.20/0.59  
% 0.20/0.59  # -------------------------------------------------
% 0.20/0.59  # User time                : 0.319 s
% 0.20/0.59  # System time              : 0.009 s
% 0.20/0.59  # Total time               : 0.328 s
% 0.20/0.59  # Maximum resident set size: 1712 pages
% 0.20/0.59  % E---3.1 exiting
%------------------------------------------------------------------------------