TSTP Solution File: GRP503-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP503-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 00:20:43 EDT 2023

% Result   : Unsatisfiable 0.55s 0.85s
% Output   : CNFRefutation 0.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   49
%            Number of leaves      :    8
% Syntax   : Number of formulae    :  124 ( 119 unt;   5 typ;   0 def)
%            Number of atoms       :  119 ( 118 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   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  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  239 (   0 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    inverse: $i > $i ).

tff(decl_24,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_25,type,
    b2: $i ).

tff(decl_26,type,
    a2: $i ).

cnf(single_axiom,axiom,
    double_divide(double_divide(X1,inverse(double_divide(X2,X3))),double_divide(inverse(X2),inverse(double_divide(X4,double_divide(X1,X4))))) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).

cnf(prove_these_axioms_2,negated_conjecture,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).

cnf(multiply,axiom,
    multiply(X1,X2) = inverse(double_divide(X2,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).

cnf(c_0_3,axiom,
    double_divide(double_divide(X1,inverse(double_divide(X2,X3))),double_divide(inverse(X2),inverse(double_divide(X4,double_divide(X1,X4))))) = X3,
    single_axiom ).

cnf(c_0_4,plain,
    double_divide(double_divide(X1,inverse(X2)),double_divide(inverse(double_divide(X3,inverse(double_divide(X4,X2)))),inverse(double_divide(X5,double_divide(X1,X5))))) = double_divide(inverse(X4),inverse(double_divide(X6,double_divide(X3,X6)))),
    inference(spm,[status(thm)],[c_0_3,c_0_3]) ).

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

cnf(c_0_6,plain,
    inverse(double_divide(X1,double_divide(X2,X1))) = inverse(double_divide(X3,double_divide(X2,X3))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_5]),c_0_3]) ).

cnf(c_0_7,plain,
    double_divide(double_divide(X1,inverse(double_divide(X2,double_divide(X3,X2)))),double_divide(inverse(X4),inverse(double_divide(X5,double_divide(X1,X5))))) = double_divide(X3,X4),
    inference(spm,[status(thm)],[c_0_3,c_0_6]) ).

cnf(c_0_8,plain,
    double_divide(X1,double_divide(X2,double_divide(X3,X2))) = double_divide(X1,double_divide(X4,double_divide(X3,X4))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_7]) ).

cnf(c_0_9,plain,
    double_divide(X1,double_divide(X2,X1)) = double_divide(X3,double_divide(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_8]),c_0_3]) ).

cnf(c_0_10,plain,
    double_divide(X1,double_divide(X2,inverse(double_divide(X3,double_divide(X4,double_divide(X1,X4)))))) = double_divide(inverse(X3),inverse(double_divide(X5,double_divide(X2,X5)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_4]),c_0_4]),c_0_7]) ).

cnf(c_0_11,plain,
    double_divide(X1,double_divide(X2,X1)) = double_divide(double_divide(X3,X2),double_divide(X4,double_divide(X3,X4))),
    inference(spm,[status(thm)],[c_0_9,c_0_9]) ).

cnf(c_0_12,plain,
    double_divide(inverse(double_divide(X1,X2)),inverse(double_divide(X3,double_divide(X4,X3)))) = double_divide(X1,double_divide(X4,inverse(double_divide(b2,double_divide(X2,b2))))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).

cnf(c_0_13,plain,
    double_divide(double_divide(X1,inverse(double_divide(X2,X3))),double_divide(X4,double_divide(X1,inverse(double_divide(b2,double_divide(inverse(double_divide(X5,double_divide(X2,X5))),b2)))))) = double_divide(inverse(X3),inverse(double_divide(X6,double_divide(X4,X6)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_7]),c_0_12]) ).

cnf(c_0_14,plain,
    double_divide(double_divide(double_divide(X1,inverse(double_divide(X2,X3))),inverse(double_divide(X4,X5))),double_divide(inverse(X4),inverse(double_divide(double_divide(inverse(X2),inverse(double_divide(X6,double_divide(X1,X6)))),X3)))) = X5,
    inference(spm,[status(thm)],[c_0_3,c_0_3]) ).

cnf(c_0_15,plain,
    double_divide(inverse(double_divide(X1,double_divide(b2,X1))),double_divide(X2,inverse(double_divide(b2,double_divide(b2,b2))))) = double_divide(b2,double_divide(X2,b2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_13]),c_0_12]),c_0_11]) ).

cnf(c_0_16,plain,
    double_divide(inverse(X1),inverse(double_divide(double_divide(inverse(X2),inverse(double_divide(X3,double_divide(X4,X3)))),X5))) = double_divide(inverse(X1),inverse(double_divide(b2,double_divide(double_divide(X4,inverse(double_divide(X2,X5))),b2)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_14]),c_0_4]) ).

cnf(c_0_17,plain,
    double_divide(inverse(double_divide(X1,double_divide(b2,X1))),double_divide(X2,inverse(double_divide(X3,double_divide(b2,X3))))) = double_divide(b2,double_divide(X2,b2)),
    inference(spm,[status(thm)],[c_0_15,c_0_9]) ).

cnf(c_0_18,plain,
    inverse(double_divide(double_divide(inverse(X1),inverse(double_divide(X2,double_divide(X3,X2)))),X4)) = inverse(double_divide(b2,double_divide(double_divide(X3,inverse(double_divide(X1,X4))),b2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_16]),c_0_3]) ).

cnf(c_0_19,plain,
    double_divide(double_divide(X1,inverse(double_divide(double_divide(X2,X3),X4))),double_divide(X2,double_divide(X1,inverse(double_divide(b2,double_divide(X3,b2)))))) = X4,
    inference(spm,[status(thm)],[c_0_3,c_0_12]) ).

cnf(c_0_20,plain,
    double_divide(inverse(double_divide(X1,double_divide(b2,X1))),double_divide(X2,double_divide(b2,inverse(double_divide(b2,double_divide(X3,b2)))))) = double_divide(b2,double_divide(inverse(double_divide(X2,X3)),b2)),
    inference(spm,[status(thm)],[c_0_17,c_0_12]) ).

cnf(c_0_21,plain,
    double_divide(X1,double_divide(double_divide(inverse(X2),inverse(double_divide(X3,double_divide(X4,X3)))),X5)) = double_divide(X1,double_divide(b2,double_divide(double_divide(X4,inverse(double_divide(X2,X5))),b2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_18]),c_0_7]) ).

cnf(c_0_22,plain,
    double_divide(X1,double_divide(inverse(double_divide(double_divide(inverse(double_divide(b2,double_divide(X2,b2))),X2),X3)),X1)) = X3,
    inference(spm,[status(thm)],[c_0_11,c_0_19]) ).

cnf(c_0_23,plain,
    double_divide(inverse(double_divide(X1,double_divide(b2,X1))),double_divide(b2,double_divide(b2,b2))) = double_divide(b2,double_divide(inverse(double_divide(inverse(double_divide(X2,double_divide(b2,X2))),b2)),b2)),
    inference(spm,[status(thm)],[c_0_20,c_0_17]) ).

cnf(c_0_24,plain,
    double_divide(double_divide(inverse(X1),inverse(double_divide(X2,double_divide(X3,X2)))),X4) = double_divide(b2,double_divide(double_divide(X3,inverse(double_divide(X1,X4))),b2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_21]),c_0_3]) ).

cnf(c_0_25,plain,
    double_divide(b2,double_divide(inverse(double_divide(b2,double_divide(b2,b2))),b2)) = double_divide(b2,double_divide(inverse(double_divide(b2,double_divide(X1,b2))),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_9]) ).

cnf(c_0_26,plain,
    double_divide(double_divide(X1,inverse(double_divide(X2,double_divide(X3,double_divide(inverse(X2),inverse(double_divide(X4,double_divide(X1,X4)))))))),X5) = double_divide(X3,X5),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_24]),c_0_7]) ).

cnf(c_0_27,plain,
    double_divide(inverse(double_divide(inverse(double_divide(X1,double_divide(b2,X1))),b2)),inverse(X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_22]),c_0_22]) ).

cnf(c_0_28,plain,
    double_divide(inverse(double_divide(b2,double_divide(b2,b2))),b2) = double_divide(inverse(double_divide(b2,double_divide(X1,b2))),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_25]),c_0_3]) ).

cnf(c_0_29,plain,
    double_divide(double_divide(b2,inverse(double_divide(X1,double_divide(b2,double_divide(inverse(X1),b2))))),X2) = double_divide(inverse(double_divide(X3,double_divide(b2,X3))),X2),
    inference(spm,[status(thm)],[c_0_26,c_0_17]) ).

cnf(c_0_30,plain,
    double_divide(inverse(double_divide(inverse(double_divide(b2,double_divide(X1,b2))),X1)),inverse(X2)) = X2,
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_31,plain,
    double_divide(b2,double_divide(inverse(double_divide(X1,double_divide(b2,double_divide(inverse(X1),b2)))),b2)) = double_divide(inverse(double_divide(b2,double_divide(b2,b2))),double_divide(b2,double_divide(b2,b2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_29]),c_0_23]),c_0_11]) ).

cnf(c_0_32,plain,
    double_divide(inverse(double_divide(inverse(double_divide(X1,double_divide(X2,X1))),X2)),inverse(X3)) = X3,
    inference(spm,[status(thm)],[c_0_30,c_0_9]) ).

cnf(c_0_33,plain,
    double_divide(b2,double_divide(inverse(double_divide(double_divide(X1,double_divide(b2,double_divide(inverse(X1),b2))),double_divide(inverse(double_divide(b2,double_divide(b2,b2))),double_divide(b2,double_divide(b2,b2))))),b2)) = double_divide(inverse(double_divide(b2,double_divide(b2,b2))),double_divide(b2,double_divide(b2,b2))),
    inference(spm,[status(thm)],[c_0_31,c_0_31]) ).

cnf(c_0_34,plain,
    double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X1,double_divide(b2,double_divide(X2,b2)))) = X3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_32]),c_0_32]) ).

cnf(c_0_35,plain,
    double_divide(double_divide(X1,double_divide(X2,inverse(double_divide(b2,double_divide(X3,b2))))),X4) = double_divide(b2,double_divide(double_divide(X2,inverse(double_divide(double_divide(X1,X3),X4))),b2)),
    inference(spm,[status(thm)],[c_0_24,c_0_12]) ).

cnf(c_0_36,plain,
    double_divide(b2,double_divide(inverse(double_divide(inverse(double_divide(b2,double_divide(b2,b2))),double_divide(b2,double_divide(b2,b2)))),b2)) = double_divide(inverse(double_divide(b2,double_divide(b2,b2))),double_divide(b2,double_divide(b2,b2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_23]) ).

cnf(c_0_37,plain,
    double_divide(double_divide(X1,double_divide(X2,inverse(double_divide(X3,double_divide(X4,X3))))),X5) = double_divide(b2,double_divide(double_divide(X2,inverse(double_divide(double_divide(X1,X4),X5))),b2)),
    inference(spm,[status(thm)],[c_0_35,c_0_9]) ).

cnf(c_0_38,plain,
    double_divide(double_divide(double_divide(double_divide(X1,b2),X1),X2),double_divide(b2,double_divide(b2,b2))) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_11]),c_0_11]) ).

cnf(c_0_39,plain,
    double_divide(X1,double_divide(double_divide(X2,X3),X1)) = double_divide(double_divide(X4,double_divide(X2,X4)),double_divide(X5,double_divide(X3,X5))),
    inference(spm,[status(thm)],[c_0_9,c_0_11]) ).

cnf(c_0_40,plain,
    double_divide(double_divide(X1,X2),double_divide(inverse(X1),inverse(double_divide(inverse(X3),X3)))) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_27]),c_0_27]) ).

cnf(c_0_41,plain,
    double_divide(inverse(double_divide(inverse(double_divide(b2,double_divide(b2,b2))),double_divide(b2,double_divide(b2,b2)))),inverse(double_divide(inverse(double_divide(b2,double_divide(b2,b2))),double_divide(b2,double_divide(b2,b2))))) = double_divide(inverse(double_divide(b2,double_divide(b2,b2))),b2),
    inference(spm,[status(thm)],[c_0_28,c_0_36]) ).

cnf(c_0_42,plain,
    double_divide(double_divide(X1,double_divide(X2,double_divide(X3,X2))),X4) = double_divide(b2,double_divide(double_divide(double_divide(X1,X3),X4),b2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_32]),c_0_32]) ).

cnf(c_0_43,plain,
    double_divide(b2,double_divide(double_divide(X1,b2),b2)) = double_divide(X1,double_divide(double_divide(X2,b2),X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_9]),c_0_39]) ).

cnf(c_0_44,plain,
    double_divide(double_divide(b2,double_divide(double_divide(double_divide(inverse(double_divide(b2,double_divide(b2,b2))),b2),X1),b2)),double_divide(inverse(double_divide(b2,double_divide(b2,b2))),b2)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).

cnf(c_0_45,plain,
    double_divide(double_divide(X1,b2),X1) = double_divide(double_divide(X2,b2),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_43]),c_0_7]) ).

cnf(c_0_46,plain,
    double_divide(double_divide(double_divide(X1,inverse(double_divide(X2,double_divide(X3,X2)))),inverse(double_divide(X4,double_divide(X5,X4)))),double_divide(inverse(X6),inverse(double_divide(b2,double_divide(double_divide(X1,inverse(double_divide(X7,double_divide(X3,X7)))),b2))))) = double_divide(X5,X6),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_7]),c_0_24]) ).

cnf(c_0_47,plain,
    double_divide(double_divide(b2,double_divide(double_divide(b2,double_divide(X1,b2)),b2)),double_divide(inverse(double_divide(b2,double_divide(b2,b2))),b2)) = double_divide(X1,double_divide(inverse(double_divide(b2,double_divide(b2,b2))),b2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_11]),c_0_11]) ).

cnf(c_0_48,plain,
    double_divide(double_divide(double_divide(X1,b2),X1),double_divide(b2,double_divide(b2,b2))) = double_divide(b2,b2),
    inference(spm,[status(thm)],[c_0_38,c_0_45]) ).

cnf(c_0_49,plain,
    double_divide(double_divide(b2,double_divide(double_divide(b2,double_divide(X1,b2)),b2)),X2) = double_divide(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_46]) ).

cnf(c_0_50,plain,
    double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X1,double_divide(X4,double_divide(X2,X4)))) = X3,
    inference(spm,[status(thm)],[c_0_34,c_0_9]) ).

cnf(c_0_51,plain,
    double_divide(b2,double_divide(double_divide(b2,double_divide(double_divide(b2,b2),b2)),b2)) = double_divide(b2,b2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_42]),c_0_42]),c_0_48]) ).

cnf(c_0_52,plain,
    double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(X1,X2),X1),X3),X2),X4),X3) = X4,
    inference(spm,[status(thm)],[c_0_50,c_0_50]) ).

cnf(c_0_53,plain,
    double_divide(double_divide(b2,double_divide(double_divide(X1,double_divide(X2,X1)),b2)),X3) = double_divide(X2,X3),
    inference(spm,[status(thm)],[c_0_49,c_0_9]) ).

cnf(c_0_54,plain,
    double_divide(double_divide(b2,double_divide(double_divide(b2,b2),b2)),b2) = b2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_51]),c_0_3]) ).

cnf(c_0_55,plain,
    double_divide(double_divide(double_divide(X1,X2),X1),double_divide(X3,double_divide(X4,X3))) = double_divide(X2,X4),
    inference(spm,[status(thm)],[c_0_52,c_0_50]) ).

cnf(c_0_56,plain,
    double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X2)),X1)),X4) = double_divide(X3,X4),
    inference(spm,[status(thm)],[c_0_53,c_0_9]) ).

cnf(c_0_57,plain,
    double_divide(b2,double_divide(b2,double_divide(double_divide(double_divide(double_divide(b2,double_divide(b2,b2)),b2),b2),b2))) = double_divide(b2,b2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_54]),c_0_42]),c_0_42]) ).

cnf(c_0_58,plain,
    double_divide(X1,double_divide(X2,double_divide(double_divide(X3,double_divide(X4,X3)),X2))) = double_divide(X1,X4),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_55]) ).

cnf(c_0_59,plain,
    double_divide(double_divide(b2,double_divide(double_divide(X1,b2),X1)),b2) = b2,
    inference(spm,[status(thm)],[c_0_54,c_0_45]) ).

cnf(c_0_60,plain,
    double_divide(b2,double_divide(double_divide(double_divide(double_divide(b2,double_divide(b2,b2)),b2),b2),b2)) = b2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_57]),c_0_3]) ).

cnf(c_0_61,plain,
    double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X2)),X1)) = X3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_58]),c_0_44]) ).

cnf(c_0_62,plain,
    double_divide(b2,double_divide(double_divide(double_divide(inverse(double_divide(b2,double_divide(b2,b2))),b2),inverse(double_divide(double_divide(b2,b2),b2))),b2)) = b2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_28]),c_0_37]) ).

cnf(c_0_63,plain,
    double_divide(inverse(b2),double_divide(double_divide(double_divide(b2,double_divide(b2,b2)),b2),b2)) = double_divide(inverse(double_divide(b2,double_divide(b2,b2))),b2),
    inference(spm,[status(thm)],[c_0_28,c_0_60]) ).

cnf(c_0_64,plain,
    double_divide(double_divide(double_divide(X1,double_divide(X2,X1)),X3),X2) = double_divide(b2,double_divide(X3,b2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_61]),c_0_11]) ).

cnf(c_0_65,plain,
    double_divide(b2,double_divide(inverse(double_divide(b2,double_divide(b2,b2))),b2)) = inverse(double_divide(double_divide(b2,b2),b2)),
    inference(spm,[status(thm)],[c_0_44,c_0_62]) ).

cnf(c_0_66,plain,
    double_divide(inverse(double_divide(b2,double_divide(b2,b2))),b2) = double_divide(inverse(b2),double_divide(b2,double_divide(b2,b2))),
    inference(rw,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_67,plain,
    double_divide(double_divide(X1,double_divide(double_divide(X2,b2),X2)),X1) = b2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_38]),c_0_61]) ).

cnf(c_0_68,plain,
    double_divide(double_divide(inverse(X1),inverse(double_divide(inverse(X2),X2))),double_divide(X3,X1)) = X3,
    inference(spm,[status(thm)],[c_0_61,c_0_40]) ).

cnf(c_0_69,plain,
    double_divide(b2,double_divide(inverse(b2),double_divide(b2,double_divide(b2,b2)))) = inverse(double_divide(double_divide(b2,b2),b2)),
    inference(rw,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_70,plain,
    double_divide(inverse(double_divide(inverse(X1),double_divide(X2,double_divide(X1,X2)))),inverse(X3)) = X3,
    inference(spm,[status(thm)],[c_0_32,c_0_61]) ).

cnf(c_0_71,plain,
    double_divide(double_divide(inverse(b2),b2),inverse(double_divide(double_divide(b2,b2),b2))) = b2,
    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_66]),c_0_42]),c_0_42]),c_0_37]),c_0_61]) ).

cnf(c_0_72,plain,
    double_divide(double_divide(double_divide(X1,b2),X1),b2) = double_divide(b2,double_divide(b2,double_divide(b2,b2))),
    inference(spm,[status(thm)],[c_0_38,c_0_67]) ).

cnf(c_0_73,plain,
    double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X1)),X2) = X3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_11]),c_0_61]) ).

cnf(c_0_74,plain,
    double_divide(double_divide(inverse(X1),X1),inverse(double_divide(double_divide(b2,b2),b2))) = b2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).

cnf(c_0_75,plain,
    double_divide(double_divide(inverse(b2),b2),inverse(double_divide(double_divide(X1,b2),X1))) = b2,
    inference(spm,[status(thm)],[c_0_71,c_0_45]) ).

cnf(c_0_76,plain,
    double_divide(double_divide(b2,double_divide(double_divide(double_divide(inverse(b2),b2),inverse(double_divide(b2,double_divide(b2,b2)))),b2)),b2) = double_divide(b2,double_divide(b2,double_divide(b2,b2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_66]),c_0_42]) ).

cnf(c_0_77,plain,
    double_divide(double_divide(inverse(double_divide(double_divide(b2,b2),b2)),b2),inverse(X1)) = X1,
    inference(spm,[status(thm)],[c_0_73,c_0_74]) ).

cnf(c_0_78,plain,
    double_divide(double_divide(inverse(b2),b2),inverse(double_divide(b2,double_divide(double_divide(double_divide(inverse(b2),b2),inverse(double_divide(b2,double_divide(b2,b2)))),b2)))) = b2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_66]),c_0_42]) ).

cnf(c_0_79,plain,
    double_divide(double_divide(inverse(b2),b2),inverse(double_divide(b2,double_divide(b2,b2)))) = double_divide(b2,double_divide(b2,double_divide(b2,double_divide(b2,b2)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_76]),c_0_61]) ).

cnf(c_0_80,plain,
    double_divide(double_divide(inverse(double_divide(double_divide(X1,b2),X1)),b2),inverse(X2)) = X2,
    inference(spm,[status(thm)],[c_0_77,c_0_45]) ).

cnf(c_0_81,plain,
    inverse(inverse(inverse(double_divide(inverse(X1),X1)))) = inverse(double_divide(inverse(X2),X2)),
    inference(spm,[status(thm)],[c_0_40,c_0_68]) ).

cnf(c_0_82,plain,
    double_divide(b2,double_divide(X1,inverse(double_divide(b2,double_divide(double_divide(X2,b2),b2))))) = double_divide(X3,double_divide(X1,inverse(double_divide(b2,double_divide(double_divide(X2,X3),b2))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_11]),c_0_11]),c_0_12]) ).

cnf(c_0_83,plain,
    double_divide(double_divide(inverse(b2),b2),inverse(double_divide(b2,double_divide(double_divide(b2,double_divide(b2,double_divide(b2,double_divide(b2,b2)))),b2)))) = b2,
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_84,plain,
    inverse(inverse(double_divide(inverse(X1),X1))) = double_divide(inverse(X2),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_80]) ).

cnf(c_0_85,plain,
    double_divide(b2,double_divide(double_divide(inverse(b2),b2),inverse(double_divide(b2,double_divide(double_divide(b2,b2),b2))))) = double_divide(b2,double_divide(b2,double_divide(b2,double_divide(b2,b2)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_42]),c_0_72]) ).

cnf(c_0_86,plain,
    double_divide(b2,double_divide(inverse(double_divide(inverse(b2),b2)),b2)) = double_divide(inverse(b2),b2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_81]),c_0_81]),c_0_84]),c_0_84]) ).

cnf(c_0_87,plain,
    double_divide(double_divide(X1,inverse(double_divide(b2,double_divide(double_divide(X2,X3),b2)))),double_divide(b2,double_divide(X1,inverse(double_divide(b2,double_divide(double_divide(X2,b2),b2)))))) = double_divide(b2,double_divide(X3,b2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_82]),c_0_11]) ).

cnf(c_0_88,plain,
    double_divide(double_divide(inverse(b2),b2),inverse(double_divide(b2,double_divide(double_divide(b2,b2),b2)))) = double_divide(b2,double_divide(b2,double_divide(b2,b2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_85]),c_0_3]) ).

cnf(c_0_89,plain,
    double_divide(double_divide(inverse(double_divide(inverse(b2),b2)),b2),double_divide(inverse(b2),b2)) = double_divide(b2,double_divide(b2,b2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_86]),c_0_11]) ).

cnf(c_0_90,plain,
    double_divide(b2,double_divide(double_divide(double_divide(b2,b2),double_divide(b2,double_divide(b2,double_divide(b2,double_divide(b2,b2))))),b2)) = double_divide(b2,double_divide(b2,b2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_88]),c_0_42]) ).

cnf(c_0_91,plain,
    double_divide(b2,double_divide(double_divide(double_divide(double_divide(inverse(b2),b2),b2),inverse(double_divide(inverse(b2),b2))),b2)) = b2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_89]),c_0_42]) ).

cnf(c_0_92,plain,
    double_divide(double_divide(b2,double_divide(b2,b2)),double_divide(b2,b2)) = double_divide(b2,double_divide(b2,double_divide(b2,double_divide(b2,b2)))),
    inference(spm,[status(thm)],[c_0_73,c_0_90]) ).

cnf(c_0_93,plain,
    double_divide(double_divide(b2,b2),double_divide(b2,double_divide(b2,double_divide(b2,double_divide(b2,b2))))) = b2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_90]),c_0_61]) ).

cnf(c_0_94,plain,
    double_divide(b2,double_divide(double_divide(inverse(b2),b2),b2)) = inverse(double_divide(inverse(b2),b2)),
    inference(spm,[status(thm)],[c_0_73,c_0_91]) ).

cnf(c_0_95,plain,
    double_divide(double_divide(double_divide(inverse(X1),inverse(double_divide(inverse(X2),X2))),X3),X1) = X3,
    inference(spm,[status(thm)],[c_0_40,c_0_73]) ).

cnf(c_0_96,plain,
    double_divide(double_divide(double_divide(X1,X2),X1),b2) = double_divide(X2,double_divide(b2,double_divide(b2,b2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_92]),c_0_93]) ).

cnf(c_0_97,plain,
    double_divide(inverse(double_divide(inverse(b2),b2)),inverse(b2)) = b2,
    inference(spm,[status(thm)],[c_0_73,c_0_94]) ).

cnf(c_0_98,plain,
    double_divide(b2,inverse(double_divide(inverse(X1),X1))) = inverse(double_divide(double_divide(b2,b2),b2)),
    inference(spm,[status(thm)],[c_0_95,c_0_74]) ).

cnf(c_0_99,plain,
    double_divide(inverse(double_divide(double_divide(b2,b2),b2)),b2) = double_divide(inverse(b2),double_divide(b2,double_divide(b2,b2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98]) ).

cnf(c_0_100,plain,
    double_divide(b2,double_divide(X1,b2)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_99]),c_0_42]),c_0_75]),c_0_64]),c_0_64]) ).

cnf(c_0_101,plain,
    double_divide(X1,double_divide(inverse(X2),inverse(double_divide(inverse(double_divide(X2,X3)),X1)))) = X3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_73]),c_0_61]) ).

cnf(c_0_102,plain,
    double_divide(inverse(X1),X1) = double_divide(inverse(X2),X2),
    inference(spm,[status(thm)],[c_0_84,c_0_84]) ).

cnf(c_0_103,plain,
    double_divide(double_divide(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_73,c_0_100]) ).

cnf(c_0_104,plain,
    double_divide(inverse(b2),double_divide(inverse(b2),b2)) = b2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_97]),c_0_102]) ).

cnf(c_0_105,plain,
    double_divide(X1,double_divide(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_61,c_0_100]) ).

cnf(c_0_106,plain,
    double_divide(inverse(b2),b2) = double_divide(b2,inverse(b2)),
    inference(spm,[status(thm)],[c_0_103,c_0_104]) ).

cnf(c_0_107,plain,
    double_divide(inverse(X1),X1) = double_divide(b2,inverse(b2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_66]),c_0_105]),c_0_100]),c_0_106]) ).

cnf(c_0_108,negated_conjecture,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    prove_these_axioms_2 ).

cnf(c_0_109,axiom,
    multiply(X1,X2) = inverse(double_divide(X2,X1)),
    multiply ).

cnf(c_0_110,plain,
    inverse(double_divide(X1,inverse(X1))) = double_divide(b2,inverse(b2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_107]),c_0_100]),c_0_105]),c_0_103]) ).

cnf(c_0_111,plain,
    inverse(double_divide(double_divide(b2,inverse(b2)),X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_105]),c_0_100]),c_0_107]) ).

cnf(c_0_112,negated_conjecture,
    inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109]),c_0_109]) ).

cnf(c_0_113,plain,
    inverse(double_divide(b2,inverse(b2))) = double_divide(b2,inverse(b2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_100]),c_0_106]),c_0_106]) ).

cnf(c_0_114,plain,
    double_divide(double_divide(X1,inverse(X1)),inverse(X2)) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_110]),c_0_105]),c_0_111]) ).

cnf(c_0_115,negated_conjecture,
    inverse(double_divide(a2,double_divide(b2,inverse(b2)))) != a2,
    inference(spm,[status(thm)],[c_0_112,c_0_113]) ).

cnf(c_0_116,plain,
    double_divide(X1,double_divide(X2,inverse(X2))) = inverse(X1),
    inference(spm,[status(thm)],[c_0_103,c_0_114]) ).

cnf(c_0_117,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_107]),c_0_107]),c_0_113]),c_0_105]) ).

cnf(c_0_118,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_116]),c_0_117])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : GRP503-1 : TPTP v8.1.2. Released v2.6.0.
% 0.08/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 29 03:10:45 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.53/0.59  start to proof: theBenchmark
% 0.55/0.85  % Version  : CSE_E---1.5
% 0.55/0.85  % Problem  : theBenchmark.p
% 0.55/0.85  % Proof found
% 0.55/0.85  % SZS status Theorem for theBenchmark.p
% 0.55/0.85  % SZS output start Proof
% See solution above
% 0.83/0.86  % Total time : 0.253000 s
% 0.83/0.86  % SZS output end Proof
% 0.83/0.86  % Total time : 0.255000 s
%------------------------------------------------------------------------------