TSTP Solution File: LAT077-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT077-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 05:59:29 EDT 2023

% Result   : Unsatisfiable 44.24s 44.31s
% Output   : CNFRefutation 44.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   60
%            Number of leaves      :    6
% Syntax   : Number of formulae    :  196 ( 192 unt;   4 typ;   0 def)
%            Number of atoms       :  192 ( 191 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  521 (  80 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    f: ( $i * $i ) > $i ).

tff(decl_23,type,
    a: $i ).

tff(decl_24,type,
    b: $i ).

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

cnf(mol_27B1,axiom,
    f(f(f(f(X1,X2),f(X3,X2)),X4),f(X2,f(f(f(f(f(f(X1,X1),X2),X3),X3),X2),X1))) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mol_27B1) ).

cnf(modularity,negated_conjecture,
    f(a,f(b,f(a,f(c,c)))) != f(a,f(c,f(a,f(b,b)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',modularity) ).

cnf(c_0_2,axiom,
    f(f(f(f(X1,X2),f(X3,X2)),X4),f(X2,f(f(f(f(f(f(X1,X1),X2),X3),X3),X2),X1))) = X2,
    mol_27B1 ).

cnf(c_0_3,plain,
    f(X1,f(f(X2,X1),f(f(f(f(f(f(f(X3,X1),f(X3,X1)),f(X2,X1)),X4),X4),f(X2,X1)),f(X3,X1)))) = f(X2,X1),
    inference(spm,[status(thm)],[c_0_2,c_0_2]) ).

cnf(c_0_4,plain,
    f(f(X1,f(f(X2,X3),f(X4,X3))),f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2))) = X3,
    inference(spm,[status(thm)],[c_0_2,c_0_3]) ).

cnf(c_0_5,plain,
    f(X1,f(f(X2,X1),f(f(f(f(f(f(X3,X3),f(X2,X1)),f(X4,X1)),f(X4,X1)),f(X2,X1)),X3))) = f(X2,X1),
    inference(spm,[status(thm)],[c_0_2,c_0_4]) ).

cnf(c_0_6,plain,
    f(f(X1,X2),f(f(f(X3,X2),f(X1,X2)),X2)) = f(f(X3,X2),f(X1,X2)),
    inference(spm,[status(thm)],[c_0_5,c_0_4]) ).

cnf(c_0_7,plain,
    f(f(f(f(X1,X2),f(X3,X2)),X2),f(f(f(X1,X2),f(X3,X2)),X2)) = f(f(X1,X2),f(X3,X2)),
    inference(spm,[status(thm)],[c_0_6,c_0_6]) ).

cnf(c_0_8,plain,
    f(f(f(f(X1,f(X2,X1)),f(X1,f(X2,X1))),X3),f(f(f(f(f(X1,X1),f(X2,X1)),X1),X1),f(X2,X1))) = f(X2,X1),
    inference(spm,[status(thm)],[c_0_2,c_0_6]) ).

cnf(c_0_9,plain,
    f(f(f(X1,X2),f(X1,X2)),f(f(X1,X2),f(X1,X2))) = f(X1,X2),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_10,plain,
    f(f(X1,X1),f(X1,X1)) = X1,
    inference(spm,[status(thm)],[c_0_9,c_0_2]) ).

cnf(c_0_11,plain,
    f(f(f(X1,X2),f(X3,X2)),f(f(X1,X2),f(X3,X2))) = f(f(f(X1,X2),f(X3,X2)),X2),
    inference(spm,[status(thm)],[c_0_10,c_0_7]) ).

cnf(c_0_12,plain,
    f(f(X1,X2),f(X2,f(f(f(f(f(f(X1,X1),X2),X1),X1),X2),X1))) = X2,
    inference(spm,[status(thm)],[c_0_4,c_0_10]) ).

cnf(c_0_13,plain,
    f(X1,f(f(f(f(f(f(X2,X2),X1),X3),X3),X1),X2)) = f(X1,X1),
    inference(spm,[status(thm)],[c_0_11,c_0_2]) ).

cnf(c_0_14,plain,
    f(f(X1,X2),f(X2,X2)) = X2,
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_15,plain,
    f(X1,f(f(X2,X1),f(X2,X1))) = f(X2,X1),
    inference(rw,[status(thm)],[c_0_5,c_0_13]) ).

cnf(c_0_16,plain,
    f(f(X1,X1),f(X1,X2)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).

cnf(c_0_17,plain,
    f(f(X1,X2),f(X1,X1)) = X1,
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_18,plain,
    f(X1,f(f(f(X2,f(X1,X1)),X1),f(X1,X1))) = f(f(X2,f(X1,X1)),X1),
    inference(spm,[status(thm)],[c_0_6,c_0_10]) ).

cnf(c_0_19,plain,
    f(f(f(f(X1,X2),f(X3,X2)),X4),f(X2,X2)) = X2,
    inference(rw,[status(thm)],[c_0_2,c_0_13]) ).

cnf(c_0_20,plain,
    f(X1,f(f(f(f(X2,X2),X1),X1),X2)) = f(X1,X1),
    inference(spm,[status(thm)],[c_0_13,c_0_17]) ).

cnf(c_0_21,plain,
    f(f(X1,X1),f(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_16,c_0_15]) ).

cnf(c_0_22,plain,
    f(f(f(X1,X1),X1),f(f(X1,f(X1,X1)),X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_18]),c_0_10]),c_0_10]) ).

cnf(c_0_23,plain,
    f(X1,f(f(f(X2,f(X2,X2)),X1),f(X3,X2))) = f(X1,X1),
    inference(spm,[status(thm)],[c_0_13,c_0_19]) ).

cnf(c_0_24,plain,
    f(X1,f(f(f(X2,X1),X1),f(X2,X2))) = f(X1,X1),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,plain,
    f(f(f(X1,f(X1,X1)),X1),f(X1,X1)) = X1,
    inference(spm,[status(thm)],[c_0_6,c_0_22]) ).

cnf(c_0_26,plain,
    f(f(f(X1,X1),X1),X2) = f(X2,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_10]),c_0_10]),c_0_15]) ).

cnf(c_0_27,plain,
    f(f(X1,f(X1,X1)),X1) = f(X1,X1),
    inference(spm,[status(thm)],[c_0_18,c_0_25]) ).

cnf(c_0_28,plain,
    f(f(f(X1,X1),X1),f(X2,X2)) = X2,
    inference(spm,[status(thm)],[c_0_21,c_0_26]) ).

cnf(c_0_29,plain,
    f(f(f(X1,X2),f(X1,X2)),X2) = f(X1,X2),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_30,plain,
    f(f(f(X1,X1),X1),f(X1,X1)) = X1,
    inference(rw,[status(thm)],[c_0_22,c_0_27]) ).

cnf(c_0_31,plain,
    f(f(X1,f(X1,X1)),f(X2,X2)) = X2,
    inference(spm,[status(thm)],[c_0_28,c_0_21]) ).

cnf(c_0_32,plain,
    f(f(f(X1,X2),f(X3,X2)),X2) = f(X2,f(f(X1,X2),f(X3,X2))),
    inference(spm,[status(thm)],[c_0_15,c_0_7]) ).

cnf(c_0_33,plain,
    f(f(f(X1,X2),f(X1,X2)),X1) = f(X1,X2),
    inference(spm,[status(thm)],[c_0_21,c_0_16]) ).

cnf(c_0_34,plain,
    f(f(X1,f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),X2) = f(X2,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_29]),c_0_6]),c_0_30]) ).

cnf(c_0_35,plain,
    f(f(X1,X1),f(X2,f(X2,X2))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_31]),c_0_31]),c_0_14]) ).

cnf(c_0_36,plain,
    f(f(X1,f(X1,X1)),X2) = f(X2,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_13]),c_0_15]) ).

cnf(c_0_37,plain,
    f(f(f(f(f(X1,X1),X2),X2),X1),X2) = f(X2,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_20]),c_0_10]) ).

cnf(c_0_38,plain,
    f(f(f(X1,X2),f(X2,X3)),X2) = f(X2,f(f(X1,X2),f(X2,X3))),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,plain,
    f(X1,f(f(X1,X2),f(X1,X2))) = f(X1,X2),
    inference(spm,[status(thm)],[c_0_14,c_0_16]) ).

cnf(c_0_40,plain,
    f(X1,f(f(X1,X1),X2)) = f(X1,X1),
    inference(spm,[status(thm)],[c_0_13,c_0_34]) ).

cnf(c_0_41,plain,
    f(f(f(X1,f(X2,X3)),X2),f(X2,X3)) = f(f(X2,X3),f(f(X1,f(X2,X3)),X2)),
    inference(spm,[status(thm)],[c_0_32,c_0_16]) ).

cnf(c_0_42,plain,
    f(f(X1,X1),f(f(X2,X2),X2)) = X1,
    inference(spm,[status(thm)],[c_0_35,c_0_21]) ).

cnf(c_0_43,plain,
    f(f(f(X1,f(X1,X1)),X2),f(X3,X2)) = X2,
    inference(spm,[status(thm)],[c_0_21,c_0_36]) ).

cnf(c_0_44,plain,
    f(X1,f(f(f(X2,X1),X1),f(X2,X1))) = f(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_32]),c_0_15]),c_0_32]) ).

cnf(c_0_45,plain,
    f(f(X1,f(f(X2,X3),f(X4,X3))),f(X3,X3)) = X3,
    inference(rw,[status(thm)],[c_0_4,c_0_13]) ).

cnf(c_0_46,plain,
    f(f(f(X1,X2),f(X1,X3)),X1) = f(X1,f(f(X1,X2),f(X1,X3))),
    inference(spm,[status(thm)],[c_0_38,c_0_33]) ).

cnf(c_0_47,plain,
    f(X1,f(f(X2,f(X2,X2)),f(X1,X3))) = f(X1,X3),
    inference(spm,[status(thm)],[c_0_39,c_0_36]) ).

cnf(c_0_48,plain,
    f(f(X1,X2),f(f(X1,f(X1,X2)),X1)) = f(f(X1,X2),f(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_40]),c_0_14]),c_0_14]),c_0_14]),c_0_14]),c_0_14]) ).

cnf(c_0_49,plain,
    f(X1,f(X2,f(X2,X2))) = f(X1,X1),
    inference(spm,[status(thm)],[c_0_35,c_0_21]) ).

cnf(c_0_50,plain,
    f(f(X1,X2),f(X2,X1)) = f(f(X2,X1),f(X1,X2)),
    inference(spm,[status(thm)],[c_0_41,c_0_21]) ).

cnf(c_0_51,plain,
    f(X1,f(f(X2,X2),X2)) = f(X1,X1),
    inference(spm,[status(thm)],[c_0_42,c_0_21]) ).

cnf(c_0_52,plain,
    f(f(f(X1,X2),X2),f(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).

cnf(c_0_53,plain,
    f(f(f(X1,f(X1,X1)),f(X2,X3)),X2) = f(X2,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_36]),c_0_47]) ).

cnf(c_0_54,plain,
    f(X1,f(f(f(f(X2,X2),X2),X1),X2)) = f(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_17]),c_0_10]) ).

cnf(c_0_55,plain,
    f(f(a,f(a,a)),f(a,f(a,a))) = f(f(X1,f(X1,X1)),f(X1,f(X1,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_21]),c_0_49]),c_0_26]),c_0_50]),c_0_51]) ).

cnf(c_0_56,plain,
    f(f(f(X1,X2),X1),f(X1,X2)) = X1,
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_57,plain,
    f(f(X1,f(X2,X1)),X1) = f(X2,X1),
    inference(spm,[status(thm)],[c_0_52,c_0_52]) ).

cnf(c_0_58,plain,
    f(f(f(X1,f(X1,X1)),X2),f(X2,X3)) = X2,
    inference(spm,[status(thm)],[c_0_16,c_0_36]) ).

cnf(c_0_59,plain,
    f(f(f(f(f(X1,X1),X1),X2),X1),X2) = f(X2,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_54]),c_0_10]) ).

cnf(c_0_60,plain,
    f(a,f(a,a)) = f(X1,f(X1,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_55]),c_0_42]) ).

cnf(c_0_61,plain,
    f(f(X1,X2),f(X2,f(X1,X2))) = X2,
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_62,plain,
    f(f(X1,f(X1,X2)),X1) = f(X1,X2),
    inference(spm,[status(thm)],[c_0_52,c_0_58]) ).

cnf(c_0_63,plain,
    f(X1,f(f(X1,X2),X1)) = f(X1,X2),
    inference(spm,[status(thm)],[c_0_56,c_0_56]) ).

cnf(c_0_64,plain,
    f(f(X1,X1),X1) = f(a,f(a,a)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_49]),c_0_26]),c_0_17]),c_0_16]) ).

cnf(c_0_65,plain,
    f(X1,f(f(X1,f(f(X2,X2),X1)),X2)) = f(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_61]),c_0_62]) ).

cnf(c_0_66,plain,
    f(f(X1,X1),f(f(X2,X1),f(X3,X1))) = f(a,f(a,a)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_45]),c_0_64]) ).

cnf(c_0_67,plain,
    f(f(f(f(X1,X2),f(X3,X2)),X2),f(X3,X2)) = f(f(X1,X2),f(X3,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_11]),c_0_7]) ).

cnf(c_0_68,plain,
    f(f(X1,f(X2,f(X3,X1))),f(X3,X1)) = f(f(X3,X1),f(X1,f(X2,f(X3,X1)))),
    inference(spm,[status(thm)],[c_0_32,c_0_21]) ).

cnf(c_0_69,plain,
    f(X1,f(f(X1,f(X2,X1)),f(X2,X1))) = f(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_32]),c_0_15]) ).

cnf(c_0_70,plain,
    f(f(X1,X1),f(f(X1,X2),f(X3,X1))) = f(a,f(a,a)),
    inference(spm,[status(thm)],[c_0_66,c_0_53]) ).

cnf(c_0_71,plain,
    f(f(X1,X2),f(X2,f(f(X3,X2),f(X1,X2)))) = f(f(X3,X2),f(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_32]),c_0_68]) ).

cnf(c_0_72,plain,
    f(X1,f(f(X2,X1),X1)) = f(X2,X1),
    inference(spm,[status(thm)],[c_0_56,c_0_52]) ).

cnf(c_0_73,plain,
    f(f(X1,f(X2,X1)),f(X2,X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_69]),c_0_70]),c_0_31]) ).

cnf(c_0_74,plain,
    f(X1,f(f(X1,X2),f(f(X3,f(X1,X2)),X1))) = f(f(X3,f(X1,X2)),X1),
    inference(spm,[status(thm)],[c_0_71,c_0_58]) ).

cnf(c_0_75,plain,
    f(f(X1,X2),X2) = f(X2,f(X1,X2)),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_76,plain,
    f(f(f(X1,f(X2,X1)),f(X2,X3)),X2) = f(X2,X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_13]),c_0_39]),c_0_16]),c_0_75]) ).

cnf(c_0_77,plain,
    f(X1,X2) = f(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_75]),c_0_61]) ).

cnf(c_0_78,plain,
    f(X1,f(f(X2,f(X1,X2)),f(X1,X3))) = f(X1,X3),
    inference(rw,[status(thm)],[c_0_76,c_0_77]) ).

cnf(c_0_79,plain,
    f(X1,f(f(X2,f(X2,X1)),f(X1,X3))) = f(X1,X3),
    inference(spm,[status(thm)],[c_0_78,c_0_77]) ).

cnf(c_0_80,plain,
    f(f(X1,X2),f(f(X3,f(X3,X3)),X1)) = X1,
    inference(spm,[status(thm)],[c_0_17,c_0_36]) ).

cnf(c_0_81,plain,
    f(f(X1,X1),f(f(X2,X1),f(X1,X3))) = f(a,f(a,a)),
    inference(spm,[status(thm)],[c_0_66,c_0_53]) ).

cnf(c_0_82,plain,
    f(X1,f(f(X1,f(X2,X1)),f(X2,X2))) = f(X1,X1),
    inference(spm,[status(thm)],[c_0_65,c_0_21]) ).

cnf(c_0_83,plain,
    f(f(X1,X2),f(X1,f(X3,f(X3,f(X1,X2))))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_77]) ).

cnf(c_0_84,plain,
    f(f(X1,X1),f(f(X1,X2),f(X1,X3))) = f(a,f(a,a)),
    inference(spm,[status(thm)],[c_0_81,c_0_53]) ).

cnf(c_0_85,plain,
    f(f(X1,X2),f(X1,f(X1,X2))) = X1,
    inference(spm,[status(thm)],[c_0_56,c_0_62]) ).

cnf(c_0_86,plain,
    f(f(X1,X1),f(f(f(X2,X1),f(X3,X1)),X4)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_19]),c_0_64]),c_0_31]),c_0_14]) ).

cnf(c_0_87,plain,
    f(f(f(X1,f(X1,X1)),f(X2,f(X2,X2))),X3) = f(X2,f(X2,X2)),
    inference(spm,[status(thm)],[c_0_58,c_0_31]) ).

cnf(c_0_88,plain,
    f(f(X1,f(X1,X2)),f(f(X1,X2),f(X1,X3))) = f(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_35]),c_0_77]),c_0_77]) ).

cnf(c_0_89,plain,
    f(X1,f(X1,f(X1,X2))) = f(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_85]),c_0_62]) ).

cnf(c_0_90,plain,
    f(f(f(f(X1,X2),f(X3,X1)),X4),f(X1,X1)) = X1,
    inference(spm,[status(thm)],[c_0_19,c_0_53]) ).

cnf(c_0_91,plain,
    f(f(X1,X1),f(f(f(X2,f(X2,X2)),f(X3,X1)),X4)) = X1,
    inference(spm,[status(thm)],[c_0_86,c_0_87]) ).

cnf(c_0_92,plain,
    f(f(X1,X2),f(f(X1,f(X1,X2)),f(X1,X3))) = f(X1,f(X1,X2)),
    inference(spm,[status(thm)],[c_0_88,c_0_89]) ).

cnf(c_0_93,plain,
    f(X1,f(X2,f(X1,X1))) = f(X1,X1),
    inference(spm,[status(thm)],[c_0_40,c_0_15]) ).

cnf(c_0_94,plain,
    f(f(X1,X2),f(X1,f(X3,f(f(X1,X2),X3)))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_80]),c_0_77]) ).

cnf(c_0_95,plain,
    f(f(X1,X1),f(f(f(X1,X2),f(X3,X1)),X4)) = X1,
    inference(rw,[status(thm)],[c_0_90,c_0_77]) ).

cnf(c_0_96,plain,
    f(X1,f(f(X2,X1),f(X1,f(X3,f(X2,X1))))) = f(X1,f(X3,f(X2,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_43]),c_0_77]),c_0_77]) ).

cnf(c_0_97,plain,
    f(f(f(X1,X2),f(X1,X2)),f(f(X1,X1),X3)) = f(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).

cnf(c_0_98,plain,
    f(f(X1,f(X1,X2)),f(f(X1,X2),f(X3,X1))) = f(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_77]),c_0_77]) ).

cnf(c_0_99,plain,
    f(X1,f(f(f(X2,X2),X1),f(X1,f(X2,X3)))) = f(X1,f(X2,X3)),
    inference(spm,[status(thm)],[c_0_96,c_0_97]) ).

cnf(c_0_100,plain,
    f(f(X1,X2),f(f(X1,f(X1,X2)),f(X3,X1))) = f(X1,f(X1,X2)),
    inference(spm,[status(thm)],[c_0_98,c_0_89]) ).

cnf(c_0_101,plain,
    f(X1,f(f(f(X2,X2),X1),f(f(X2,X3),X1))) = f(f(X2,X3),X1),
    inference(spm,[status(thm)],[c_0_99,c_0_77]) ).

cnf(c_0_102,plain,
    f(f(f(X1,X2),f(X1,X2)),f(f(X2,X2),X3)) = f(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_100]),c_0_93]) ).

cnf(c_0_103,plain,
    f(X1,f(f(X1,X2),f(X2,X1))) = f(X2,X1),
    inference(spm,[status(thm)],[c_0_74,c_0_43]) ).

cnf(c_0_104,plain,
    f(f(f(X1,X1),X2),f(f(X1,X3),X2)) = f(f(a,f(a,a)),f(f(X1,X3),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_101]),c_0_49]),c_0_77]) ).

cnf(c_0_105,plain,
    f(f(f(f(X1,X2),f(X2,X3)),X4),f(X2,X2)) = X2,
    inference(spm,[status(thm)],[c_0_19,c_0_53]) ).

cnf(c_0_106,plain,
    f(X1,f(f(f(X2,X2),X1),f(X1,f(X3,X2)))) = f(X1,f(X3,X2)),
    inference(spm,[status(thm)],[c_0_96,c_0_102]) ).

cnf(c_0_107,plain,
    f(f(f(X1,X2),X3),f(f(X1,X1),X3)) = f(f(a,f(a,a)),f(f(X1,X2),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_58]),c_0_104]) ).

cnf(c_0_108,plain,
    f(f(X1,X1),f(f(f(X2,X1),f(X1,X3)),X4)) = X1,
    inference(rw,[status(thm)],[c_0_105,c_0_77]) ).

cnf(c_0_109,plain,
    f(X1,f(f(f(X2,X2),X1),f(f(X3,X2),X1))) = f(f(X3,X2),X1),
    inference(spm,[status(thm)],[c_0_106,c_0_77]) ).

cnf(c_0_110,plain,
    f(X1,f(f(X1,f(X2,X1)),f(f(X3,f(X3,X3)),X2))) = f(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_36]),c_0_75]) ).

cnf(c_0_111,plain,
    f(f(f(X1,X2),X3),f(X3,f(X1,X1))) = f(f(a,f(a,a)),f(f(X1,X2),X3)),
    inference(spm,[status(thm)],[c_0_107,c_0_77]) ).

cnf(c_0_112,plain,
    f(X1,f(f(X2,f(X2,X2)),f(X3,X1))) = f(X3,X1),
    inference(spm,[status(thm)],[c_0_15,c_0_36]) ).

cnf(c_0_113,plain,
    f(f(X1,f(X2,X1)),f(f(X2,X1),f(X1,X3))) = f(X2,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_108]),c_0_77]),c_0_77]) ).

cnf(c_0_114,plain,
    f(f(f(X1,X1),X2),f(f(X3,X1),X2)) = f(f(a,f(a,a)),f(f(X3,X1),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_109]),c_0_49]),c_0_77]) ).

cnf(c_0_115,plain,
    f(f(X1,f(X2,X1)),f(f(X3,f(X3,X3)),X2)) = f(f(f(X3,f(X3,X3)),X2),f(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_110]),c_0_111]),c_0_112]) ).

cnf(c_0_116,plain,
    f(X1,f(f(X1,f(X1,X2)),f(f(X1,X2),X3))) = f(X1,f(X1,X2)),
    inference(spm,[status(thm)],[c_0_113,c_0_85]) ).

cnf(c_0_117,plain,
    f(f(X1,f(X1,X1)),f(f(X2,f(X2,X2)),X3)) = X3,
    inference(spm,[status(thm)],[c_0_31,c_0_36]) ).

cnf(c_0_118,plain,
    f(X1,f(f(f(X2,f(X2,X2)),X1),X3)) = f(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_35]),c_0_31]) ).

cnf(c_0_119,plain,
    f(f(X1,X2),f(f(f(X1,X3),f(X1,X3)),X2)) = f(f(a,f(a,a)),f(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_58]),c_0_77]) ).

cnf(c_0_120,plain,
    f(X1,f(X2,f(f(X1,X1),X2))) = f(X1,f(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]),c_0_118]),c_0_117]),c_0_77]),c_0_117]) ).

cnf(c_0_121,plain,
    f(f(X1,X2),f(X2,f(f(X1,X3),f(X1,X3)))) = f(f(a,f(a,a)),f(X1,X2)),
    inference(spm,[status(thm)],[c_0_119,c_0_77]) ).

cnf(c_0_122,plain,
    f(X1,f(X2,f(X2,f(X1,X1)))) = f(X1,f(X2,X2)),
    inference(spm,[status(thm)],[c_0_120,c_0_77]) ).

cnf(c_0_123,plain,
    f(f(X1,f(X1,X1)),X2) = f(X2,f(X3,f(X3,X3))),
    inference(spm,[status(thm)],[c_0_36,c_0_49]) ).

cnf(c_0_124,plain,
    f(f(X1,X2),f(X1,f(f(X2,X3),f(X2,X3)))) = f(f(a,f(a,a)),f(X1,X2)),
    inference(spm,[status(thm)],[c_0_121,c_0_77]) ).

cnf(c_0_125,plain,
    f(f(a,f(a,a)),f(f(X1,X2),f(X3,X1))) = f(X1,f(f(X1,X2),f(X3,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_95]),c_0_75]),c_0_14]),c_0_77]),c_0_123]) ).

cnf(c_0_126,plain,
    f(f(X1,X2),f(f(X3,f(X3,X3)),X2)) = X2,
    inference(spm,[status(thm)],[c_0_14,c_0_36]) ).

cnf(c_0_127,plain,
    f(X1,f(f(X1,X2),f(X1,f(X3,f(X1,X2))))) = f(X1,f(X3,f(X1,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_16]),c_0_77]),c_0_77]) ).

cnf(c_0_128,plain,
    f(f(X1,X2),f(X1,f(f(X2,X3),f(X4,X2)))) = f(f(a,f(a,a)),f(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126]) ).

cnf(c_0_129,plain,
    f(f(X1,X2),f(X2,f(X3,f(f(X1,X2),X3)))) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_126]),c_0_77]) ).

cnf(c_0_130,plain,
    f(f(X1,X2),X1) = f(X1,f(X1,X2)),
    inference(spm,[status(thm)],[c_0_75,c_0_56]) ).

cnf(c_0_131,plain,
    f(X1,f(f(X2,X3),f(X1,X2))) = f(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_47]) ).

cnf(c_0_132,plain,
    f(f(X1,f(X2,X1)),f(f(X3,X1),f(X2,X1))) = f(X2,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_86]),c_0_75]),c_0_77]) ).

cnf(c_0_133,plain,
    f(f(X1,f(X1,X2)),f(f(X3,X1),f(X1,X2))) = f(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_108]),c_0_130]),c_0_77]) ).

cnf(c_0_134,plain,
    f(X1,f(X2,f(X1,f(X2,X3)))) = f(X1,f(X2,X3)),
    inference(spm,[status(thm)],[c_0_131,c_0_80]) ).

cnf(c_0_135,plain,
    f(X1,f(X2,f(X1,f(X3,f(f(f(X2,X2),X1),X3))))) = f(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_77]),c_0_75]),c_0_77]) ).

cnf(c_0_136,plain,
    f(f(X1,f(X2,X1)),f(X1,f(X3,f(X2,X1)))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_43]),c_0_77]),c_0_77]) ).

cnf(c_0_137,plain,
    f(f(X1,X2),f(f(X3,X1),f(X1,f(X1,X2)))) = f(X1,f(X1,X2)),
    inference(spm,[status(thm)],[c_0_133,c_0_89]) ).

cnf(c_0_138,plain,
    f(X1,f(X2,f(X3,f(f(f(X1,X1),X2),X3)))) = f(X1,f(X2,X2)),
    inference(spm,[status(thm)],[c_0_134,c_0_135]) ).

cnf(c_0_139,plain,
    f(f(X1,f(f(X2,X2),X1)),f(X1,f(X3,X2))) = X1,
    inference(spm,[status(thm)],[c_0_136,c_0_102]) ).

cnf(c_0_140,plain,
    f(f(X1,f(X2,X1)),f(X2,X2)) = f(f(X2,X2),f(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_137]),c_0_89]),c_0_14]),c_0_89]),c_0_89]) ).

cnf(c_0_141,plain,
    f(X1,f(f(X2,X3),f(X1,X3))) = f(X1,X3),
    inference(spm,[status(thm)],[c_0_131,c_0_103]) ).

cnf(c_0_142,plain,
    f(f(X1,X1),f(X2,f(X3,f(f(X1,X2),X3)))) = f(f(X1,X1),f(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_40]),c_0_40]) ).

cnf(c_0_143,plain,
    f(f(X1,X2),f(f(f(X2,X2),X3),f(X1,X2))) = f(f(X2,X2),X3),
    inference(spm,[status(thm)],[c_0_61,c_0_102]) ).

cnf(c_0_144,plain,
    f(f(X1,f(X1,X2)),f(X2,X2)) = f(f(X2,X2),f(X1,X1)),
    inference(spm,[status(thm)],[c_0_140,c_0_77]) ).

cnf(c_0_145,plain,
    f(X1,f(f(X1,X2),f(X3,X2))) = f(X1,X2),
    inference(spm,[status(thm)],[c_0_141,c_0_77]) ).

cnf(c_0_146,plain,
    f(X1,f(f(X2,X3),f(X2,X1))) = f(X2,X1),
    inference(spm,[status(thm)],[c_0_131,c_0_77]) ).

cnf(c_0_147,plain,
    f(f(X1,X2),f(X1,f(f(f(X3,X2),f(X4,X2)),X1))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_86]),c_0_77]) ).

cnf(c_0_148,plain,
    f(f(f(X1,X2),f(X1,X2)),f(f(X3,X2),f(X3,X2))) = f(f(f(X1,X2),f(X1,X2)),f(X2,f(X3,X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_86]),c_0_75]) ).

cnf(c_0_149,plain,
    f(f(X1,X2),f(f(X1,X2),f(f(X2,X2),X3))) = f(f(X2,X2),X3),
    inference(spm,[status(thm)],[c_0_89,c_0_143]) ).

cnf(c_0_150,plain,
    f(f(X1,f(X1,X2)),f(X2,f(f(X1,X2),f(X3,X2)))) = f(f(X2,f(f(X1,X2),f(X3,X2))),f(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_11]),c_0_77]),c_0_11]),c_0_77]) ).

cnf(c_0_151,plain,
    f(X1,f(X2,f(f(X2,X3),X1))) = f(f(X2,X3),X1),
    inference(spm,[status(thm)],[c_0_146,c_0_80]) ).

cnf(c_0_152,plain,
    f(f(f(X1,X2),f(X1,X2)),f(X2,f(X3,X2))) = f(f(f(X1,X2),f(X1,X2)),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_147]),c_0_148]) ).

cnf(c_0_153,plain,
    f(X1,f(f(X1,X2),f(X1,f(f(X1,X2),X3)))) = f(X1,f(f(X1,X2),X3)),
    inference(spm,[status(thm)],[c_0_127,c_0_77]) ).

cnf(c_0_154,plain,
    f(f(X1,f(f(X2,X3),f(X4,X3))),X3) = f(X3,f(X1,f(f(X2,X3),f(X4,X3)))),
    inference(spm,[status(thm)],[c_0_130,c_0_45]) ).

cnf(c_0_155,plain,
    f(X1,f(f(X1,X2),f(X2,X3))) = f(X1,X2),
    inference(spm,[status(thm)],[c_0_131,c_0_77]) ).

cnf(c_0_156,plain,
    f(f(X1,X2),f(f(X1,X2),f(X3,f(X2,X2)))) = f(X3,f(X2,X2)),
    inference(spm,[status(thm)],[c_0_149,c_0_15]) ).

cnf(c_0_157,plain,
    f(f(X1,f(X1,X2)),f(X2,f(f(X1,X2),X3))) = f(f(X2,f(f(X1,X2),X3)),f(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_77]),c_0_77]) ).

cnf(c_0_158,plain,
    f(f(f(X1,X2),f(X1,X2)),f(X2,f(X2,X3))) = f(f(f(X1,X2),f(X1,X2)),X3),
    inference(spm,[status(thm)],[c_0_152,c_0_77]) ).

cnf(c_0_159,plain,
    f(X1,f(f(X1,X2),f(X1,f(f(X2,X2),X3)))) = f(X1,f(f(X2,X2),X3)),
    inference(spm,[status(thm)],[c_0_153,c_0_143]) ).

cnf(c_0_160,plain,
    f(X1,f(X1,f(X2,f(f(X3,X1),f(X4,X1))))) = f(X2,f(f(X3,X1),f(X4,X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_45]),c_0_154]) ).

cnf(c_0_161,plain,
    f(X1,f(f(X1,f(X2,X3)),f(X4,f(X3,X3)))) = f(X1,f(X2,X3)),
    inference(spm,[status(thm)],[c_0_155,c_0_156]) ).

cnf(c_0_162,plain,
    f(X1,f(f(X1,f(f(X2,X1),X3)),f(X2,X2))) = f(X1,f(f(X2,X1),X3)),
    inference(spm,[status(thm)],[c_0_79,c_0_157]) ).

cnf(c_0_163,plain,
    f(f(X1,X1),f(f(X1,X2),f(f(X1,X2),X3))) = f(f(X1,X1),X3),
    inference(spm,[status(thm)],[c_0_158,c_0_58]) ).

cnf(c_0_164,plain,
    f(f(X1,X1),f(f(X2,X1),f(X3,f(X3,X3)))) = f(a,f(a,a)),
    inference(spm,[status(thm)],[c_0_66,c_0_49]) ).

cnf(c_0_165,plain,
    f(f(X1,f(X2,f(X2,X2))),f(X3,f(X3,X3))) = X1,
    inference(spm,[status(thm)],[c_0_35,c_0_49]) ).

cnf(c_0_166,plain,
    f(X1,f(f(X1,X2),f(X1,f(X3,f(X2,X2))))) = f(X1,f(X3,f(X2,X2))),
    inference(spm,[status(thm)],[c_0_159,c_0_15]) ).

cnf(c_0_167,plain,
    f(X1,f(X2,f(f(X3,X2),X1))) = f(f(X3,X2),X1),
    inference(spm,[status(thm)],[c_0_146,c_0_126]) ).

cnf(c_0_168,plain,
    f(X1,f(X2,f(f(X3,f(X3,X3)),X1))) = f(f(X3,f(X3,X3)),X1),
    inference(spm,[status(thm)],[c_0_93,c_0_36]) ).

cnf(c_0_169,plain,
    f(f(a,f(a,a)),f(f(X1,X2),f(X2,X1))) = f(X1,X2),
    inference(spm,[status(thm)],[c_0_125,c_0_155]) ).

cnf(c_0_170,plain,
    f(X1,f(X2,f(X1,f(X3,f(f(X4,X2),f(X5,X2)))))) = f(X1,f(X3,f(f(X4,X2),f(X5,X2)))),
    inference(spm,[status(thm)],[c_0_134,c_0_160]) ).

cnf(c_0_171,plain,
    f(X1,f(f(X1,f(f(X2,X1),X3)),f(X4,X2))) = f(X1,f(f(X2,X1),X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_10]) ).

cnf(c_0_172,plain,
    f(f(X1,X1),f(X2,f(f(X1,X3),f(X2,X4)))) = f(f(X1,X1),f(X2,X4)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_134]),c_0_163]) ).

cnf(c_0_173,plain,
    f(f(X1,X1),f(f(X2,X1),f(f(X1,X1),X3))) = f(f(X1,X1),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_164]),c_0_165]) ).

cnf(c_0_174,plain,
    f(X1,f(f(X1,X2),f(f(X3,f(X2,X2)),X1))) = f(f(X3,f(X2,X2)),X1),
    inference(spm,[status(thm)],[c_0_166,c_0_77]) ).

cnf(c_0_175,plain,
    f(X1,f(f(X1,f(X2,X3)),f(f(X3,X3),X1))) = f(X1,f(X2,X3)),
    inference(spm,[status(thm)],[c_0_106,c_0_77]) ).

cnf(c_0_176,plain,
    f(f(X1,X2),f(X2,f(X3,f(f(X2,X1),X3)))) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_94]),c_0_77]) ).

cnf(c_0_177,plain,
    f(f(f(X1,X2),f(X2,X1)),f(X3,f(X1,X2))) = f(X1,X2),
    inference(spm,[status(thm)],[c_0_168,c_0_169]) ).

cnf(c_0_178,plain,
    f(X1,f(X1,f(X2,X1))) = f(X2,X1),
    inference(rw,[status(thm)],[c_0_72,c_0_75]) ).

cnf(c_0_179,plain,
    f(X1,f(X1,X1)) = f(X2,f(X2,X2)),
    inference(spm,[status(thm)],[c_0_60,c_0_60]) ).

cnf(c_0_180,plain,
    f(X1,f(X2,f(X1,f(f(f(X3,X2),X1),X4)))) = f(X1,f(f(f(X3,X2),X1),X4)),
    inference(spm,[status(thm)],[c_0_170,c_0_171]) ).

cnf(c_0_181,plain,
    f(X1,f(X2,f(f(f(X1,X1),X3),f(X2,X4)))) = f(X1,f(X2,X4)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_14]),c_0_14]) ).

cnf(c_0_182,plain,
    f(X1,f(f(X2,f(X2,X2)),X3)) = f(f(X3,X3),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_118]),c_0_175]) ).

cnf(c_0_183,plain,
    f(f(f(X1,X2),f(X2,X1)),f(X3,f(X2,X1))) = f(X2,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_75]),c_0_178]) ).

cnf(c_0_184,plain,
    f(f(X1,f(X1,X1)),f(f(X2,X3),f(X3,X2))) = f(X2,X3),
    inference(spm,[status(thm)],[c_0_169,c_0_179]) ).

cnf(c_0_185,plain,
    f(X1,f(f(f(X2,X2),X1),f(X1,X3))) = f(X1,f(X2,f(X1,X3))),
    inference(spm,[status(thm)],[c_0_180,c_0_181]) ).

cnf(c_0_186,plain,
    f(X1,f(X2,X3)) = f(f(X3,X2),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_183]),c_0_184]) ).

cnf(c_0_187,plain,
    f(X1,f(X2,f(X3,f(X3,X3)))) = f(f(X2,X2),X1),
    inference(spm,[status(thm)],[c_0_182,c_0_77]) ).

cnf(c_0_188,plain,
    f(X1,f(f(X2,X1),f(f(X3,X3),X1))) = f(X1,f(X3,f(X1,X2))),
    inference(spm,[status(thm)],[c_0_185,c_0_186]) ).

cnf(c_0_189,negated_conjecture,
    f(a,f(b,f(a,f(c,c)))) != f(a,f(c,f(a,f(b,b)))),
    modularity ).

cnf(c_0_190,plain,
    f(X1,f(X2,f(X1,f(X3,X3)))) = f(X1,f(X3,f(f(X2,X2),X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_187]),c_0_188]) ).

cnf(c_0_191,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_189,c_0_190]),c_0_77])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT077-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n010.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Aug 24 09:58:35 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 44.24/44.31  % Version  : CSE_E---1.5
% 44.24/44.31  % Problem  : theBenchmark.p
% 44.24/44.31  % Proof found
% 44.24/44.31  % SZS status Theorem for theBenchmark.p
% 44.24/44.31  % SZS output start Proof
% See solution above
% 44.24/44.32  % Total time : 43.732000 s
% 44.24/44.32  % SZS output end Proof
% 44.24/44.32  % Total time : 43.737000 s
%------------------------------------------------------------------------------