TSTP Solution File: RNG009-7 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG009-7 : TPTP v8.1.2. Released v1.0.0.
% 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 13:48:27 EDT 2023

% Result   : Unsatisfiable 0.85s 0.97s
% Output   : CNFRefutation 0.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  119 ( 112 unt;   7 typ;   0 def)
%            Number of atoms       :  112 ( 111 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    :    6 (   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    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  127 (   9 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    additive_identity: $i ).

tff(decl_23,type,
    add: ( $i * $i ) > $i ).

tff(decl_24,type,
    additive_inverse: $i > $i ).

tff(decl_25,type,
    multiply: ( $i * $i ) > $i ).

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

tff(decl_27,type,
    b: $i ).

tff(decl_28,type,
    c: $i ).

cnf(associativity_for_addition,axiom,
    add(X1,add(X2,X3)) = add(add(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',associativity_for_addition) ).

cnf(right_additive_inverse,axiom,
    add(X1,additive_inverse(X1)) = additive_identity,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',right_additive_inverse) ).

cnf(left_additive_identity,axiom,
    add(additive_identity,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',left_additive_identity) ).

cnf(right_additive_identity,axiom,
    add(X1,additive_identity) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',right_additive_identity) ).

cnf(distribute1,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',distribute1) ).

cnf(a_times_b_is_c,negated_conjecture,
    multiply(a,b) = c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).

cnf(commutativity_for_addition,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',commutativity_for_addition) ).

cnf(x_cubed_is_x,hypothesis,
    multiply(X1,multiply(X1,X1)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_x) ).

cnf(distribute2,axiom,
    multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',distribute2) ).

cnf(associativity_for_multiplication,axiom,
    multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',associativity_for_multiplication) ).

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

cnf(c_0_11,axiom,
    add(X1,add(X2,X3)) = add(add(X1,X2),X3),
    associativity_for_addition ).

cnf(c_0_12,axiom,
    add(X1,additive_inverse(X1)) = additive_identity,
    right_additive_inverse ).

cnf(c_0_13,axiom,
    add(additive_identity,X1) = X1,
    left_additive_identity ).

cnf(c_0_14,plain,
    add(X1,add(additive_inverse(X1),X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).

cnf(c_0_15,axiom,
    add(X1,additive_identity) = X1,
    right_additive_identity ).

cnf(c_0_16,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    distribute1 ).

cnf(c_0_17,negated_conjecture,
    multiply(a,b) = c,
    a_times_b_is_c ).

cnf(c_0_18,axiom,
    add(X1,X2) = add(X2,X1),
    commutativity_for_addition ).

cnf(c_0_19,plain,
    additive_inverse(additive_inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    multiply(a,add(X1,b)) = add(c,multiply(a,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

cnf(c_0_21,hypothesis,
    multiply(X1,multiply(X1,X1)) = X1,
    x_cubed_is_x ).

cnf(c_0_22,plain,
    add(additive_inverse(X1),add(X1,X2)) = X2,
    inference(spm,[status(thm)],[c_0_14,c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    add(c,multiply(a,additive_identity)) = c,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_13]),c_0_17]) ).

cnf(c_0_24,axiom,
    multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
    distribute2 ).

cnf(c_0_25,hypothesis,
    multiply(X1,add(X2,multiply(X1,X1))) = add(X1,multiply(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_21]),c_0_18]) ).

cnf(c_0_26,negated_conjecture,
    multiply(a,add(b,X1)) = add(c,multiply(a,X1)),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_27,negated_conjecture,
    multiply(a,additive_identity) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18]),c_0_12]) ).

cnf(c_0_28,hypothesis,
    multiply(add(X1,X2),multiply(X2,X2)) = add(X2,multiply(X1,multiply(X2,X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_18]) ).

cnf(c_0_29,hypothesis,
    add(X1,multiply(X1,additive_identity)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_13]),c_0_21]) ).

cnf(c_0_30,axiom,
    multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
    associativity_for_multiplication ).

cnf(c_0_31,negated_conjecture,
    add(c,multiply(a,additive_inverse(b))) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_12]),c_0_27]) ).

cnf(c_0_32,hypothesis,
    add(X1,multiply(additive_identity,multiply(X1,X1))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_13]),c_0_21]) ).

cnf(c_0_33,hypothesis,
    multiply(X1,additive_identity) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_29]),c_0_18]),c_0_12]) ).

cnf(c_0_34,hypothesis,
    multiply(X1,multiply(X1,multiply(X1,X2))) = multiply(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_21]),c_0_30]) ).

cnf(c_0_35,negated_conjecture,
    multiply(a,additive_inverse(b)) = additive_inverse(c),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_31]),c_0_15]) ).

cnf(c_0_36,hypothesis,
    multiply(additive_identity,multiply(X1,X1)) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_18]),c_0_12]) ).

cnf(c_0_37,hypothesis,
    multiply(X1,multiply(additive_identity,X2)) = multiply(additive_identity,X2),
    inference(spm,[status(thm)],[c_0_30,c_0_33]) ).

cnf(c_0_38,plain,
    add(X1,add(X2,additive_inverse(X1))) = X2,
    inference(spm,[status(thm)],[c_0_14,c_0_18]) ).

cnf(c_0_39,plain,
    add(multiply(X1,X2),add(multiply(X1,X3),X4)) = add(multiply(X1,add(X2,X3)),X4),
    inference(spm,[status(thm)],[c_0_11,c_0_16]) ).

cnf(c_0_40,negated_conjecture,
    multiply(add(c,multiply(a,X1)),X2) = multiply(a,multiply(add(X1,b),X2)),
    inference(spm,[status(thm)],[c_0_30,c_0_20]) ).

cnf(c_0_41,hypothesis,
    multiply(a,multiply(a,additive_inverse(c))) = additive_inverse(c),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_42,hypothesis,
    multiply(additive_identity,X1) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_37]) ).

cnf(c_0_43,plain,
    add(additive_inverse(multiply(X1,X2)),multiply(X1,add(X2,X3))) = multiply(X1,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_18]) ).

cnf(c_0_44,plain,
    add(multiply(X1,X2),add(multiply(X3,X2),X4)) = add(multiply(add(X1,X3),X2),X4),
    inference(spm,[status(thm)],[c_0_11,c_0_24]) ).

cnf(c_0_45,hypothesis,
    multiply(X1,multiply(X2,multiply(X1,multiply(X2,multiply(X1,X2))))) = multiply(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_30]),c_0_30]) ).

cnf(c_0_46,hypothesis,
    multiply(a,multiply(add(b,multiply(a,additive_inverse(c))),X1)) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_12]),c_0_42]),c_0_18]) ).

cnf(c_0_47,plain,
    multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_12]),c_0_33]),c_0_15]) ).

cnf(c_0_48,plain,
    add(additive_inverse(multiply(X1,X2)),multiply(add(X1,X3),X2)) = multiply(X3,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_44]),c_0_18]) ).

cnf(c_0_49,hypothesis,
    multiply(add(b,multiply(a,additive_inverse(c))),a) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_33]),c_0_33]),c_0_33]) ).

cnf(c_0_50,plain,
    multiply(additive_inverse(multiply(X1,X2)),X3) = multiply(X1,multiply(additive_inverse(X2),X3)),
    inference(spm,[status(thm)],[c_0_30,c_0_47]) ).

cnf(c_0_51,plain,
    multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_12]),c_0_42]),c_0_15]) ).

cnf(c_0_52,hypothesis,
    additive_inverse(multiply(a,multiply(c,a))) = additive_inverse(multiply(b,a)),
    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_48,c_0_49]),c_0_15]),c_0_47]),c_0_50]),c_0_51]),c_0_47]) ).

cnf(c_0_53,hypothesis,
    multiply(a,multiply(c,a)) = multiply(b,a),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_52]),c_0_19]) ).

cnf(c_0_54,hypothesis,
    multiply(add(b,additive_inverse(multiply(a,c))),multiply(a,X1)) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_49]),c_0_42]),c_0_47]) ).

cnf(c_0_55,negated_conjecture,
    multiply(a,multiply(b,X1)) = multiply(c,X1),
    inference(spm,[status(thm)],[c_0_30,c_0_17]) ).

cnf(c_0_56,hypothesis,
    multiply(a,multiply(c,multiply(a,X1))) = multiply(b,multiply(a,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_53]),c_0_30]),c_0_30]) ).

cnf(c_0_57,hypothesis,
    multiply(X1,add(multiply(X1,X1),X2)) = add(X1,multiply(X1,X2)),
    inference(spm,[status(thm)],[c_0_16,c_0_21]) ).

cnf(c_0_58,negated_conjecture,
    multiply(add(b,additive_inverse(multiply(a,c))),multiply(c,X1)) = additive_identity,
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_59,negated_conjecture,
    multiply(a,multiply(c,multiply(c,X1))) = multiply(b,multiply(c,X1)),
    inference(spm,[status(thm)],[c_0_56,c_0_55]) ).

cnf(c_0_60,hypothesis,
    multiply(X1,multiply(add(X1,X2),X1)) = add(X1,multiply(X1,multiply(X2,X1))),
    inference(spm,[status(thm)],[c_0_57,c_0_24]) ).

cnf(c_0_61,hypothesis,
    multiply(c,add(b,additive_inverse(multiply(a,c)))) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_58]),c_0_33]) ).

cnf(c_0_62,plain,
    add(multiply(X1,X2),multiply(X3,multiply(X4,X2))) = multiply(add(X1,multiply(X3,X4)),X2),
    inference(spm,[status(thm)],[c_0_24,c_0_30]) ).

cnf(c_0_63,hypothesis,
    multiply(b,multiply(c,c)) = multiply(a,c),
    inference(spm,[status(thm)],[c_0_59,c_0_21]) ).

cnf(c_0_64,negated_conjecture,
    multiply(a,multiply(a,multiply(c,X1))) = multiply(c,X1),
    inference(spm,[status(thm)],[c_0_34,c_0_55]) ).

cnf(c_0_65,negated_conjecture,
    multiply(a,multiply(a,c)) = c,
    inference(spm,[status(thm)],[c_0_34,c_0_17]) ).

cnf(c_0_66,plain,
    add(additive_inverse(X1),add(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_38,c_0_19]) ).

cnf(c_0_67,negated_conjecture,
    multiply(c,multiply(add(b,X1),b)) = add(c,multiply(c,multiply(X1,b))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_60]),c_0_26]),c_0_55]) ).

cnf(c_0_68,hypothesis,
    multiply(c,multiply(add(b,additive_inverse(multiply(a,c))),X1)) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_61]),c_0_42]) ).

cnf(c_0_69,hypothesis,
    multiply(add(X1,multiply(b,c)),c) = multiply(add(X1,a),c),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_24]) ).

cnf(c_0_70,negated_conjecture,
    multiply(c,multiply(a,multiply(c,multiply(a,c)))) = c,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_45]),c_0_65]) ).

cnf(c_0_71,plain,
    add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_66]),c_0_18]) ).

cnf(c_0_72,negated_conjecture,
    add(c,additive_inverse(multiply(c,multiply(a,multiply(c,b))))) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_51]),c_0_30]),c_0_47]) ).

cnf(c_0_73,plain,
    additive_inverse(additive_identity) = additive_identity,
    inference(spm,[status(thm)],[c_0_13,c_0_12]) ).

cnf(c_0_74,hypothesis,
    multiply(add(multiply(b,c),X1),c) = multiply(add(X1,a),c),
    inference(spm,[status(thm)],[c_0_69,c_0_18]) ).

cnf(c_0_75,negated_conjecture,
    multiply(c,multiply(b,multiply(a,c))) = c,
    inference(rw,[status(thm)],[c_0_70,c_0_56]) ).

cnf(c_0_76,negated_conjecture,
    multiply(c,multiply(a,multiply(c,b))) = c,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_15]),c_0_19]) ).

cnf(c_0_77,hypothesis,
    multiply(add(a,additive_inverse(multiply(b,c))),c) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_12]),c_0_42]),c_0_18]) ).

cnf(c_0_78,negated_conjecture,
    multiply(c,multiply(b,multiply(a,multiply(c,X1)))) = multiply(c,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_75]),c_0_30]),c_0_30]) ).

cnf(c_0_79,hypothesis,
    multiply(b,multiply(a,multiply(c,b))) = multiply(a,c),
    inference(spm,[status(thm)],[c_0_56,c_0_76]) ).

cnf(c_0_80,plain,
    additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
    inference(spm,[status(thm)],[c_0_71,c_0_38]) ).

cnf(c_0_81,hypothesis,
    multiply(add(a,additive_inverse(multiply(b,c))),multiply(c,X1)) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_77]),c_0_42]) ).

cnf(c_0_82,hypothesis,
    multiply(c,multiply(a,c)) = multiply(c,b),
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_83,plain,
    additive_inverse(multiply(X1,add(X2,additive_inverse(X3)))) = multiply(X1,add(X3,additive_inverse(X2))),
    inference(spm,[status(thm)],[c_0_47,c_0_80]) ).

cnf(c_0_84,hypothesis,
    multiply(c,add(a,additive_inverse(multiply(b,c)))) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_81]),c_0_33]) ).

cnf(c_0_85,hypothesis,
    multiply(c,multiply(a,multiply(c,X1))) = multiply(c,multiply(b,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_82]),c_0_30]),c_0_30]) ).

cnf(c_0_86,hypothesis,
    multiply(c,add(multiply(b,c),additive_inverse(a))) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_73]) ).

cnf(c_0_87,hypothesis,
    multiply(X1,add(multiply(X1,multiply(X1,X2)),X3)) = multiply(X1,add(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_34]),c_0_16]) ).

cnf(c_0_88,hypothesis,
    multiply(c,multiply(b,add(multiply(b,c),additive_inverse(a)))) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_33]),c_0_33]) ).

cnf(c_0_89,hypothesis,
    multiply(X1,multiply(X1,add(multiply(X1,X2),X3))) = multiply(X1,add(X2,multiply(X1,X3))),
    inference(spm,[status(thm)],[c_0_87,c_0_16]) ).

cnf(c_0_90,hypothesis,
    multiply(c,multiply(b,b)) = c,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_21]),c_0_17]) ).

cnf(c_0_91,hypothesis,
    multiply(c,multiply(b,add(c,additive_inverse(multiply(b,a))))) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_88]),c_0_33]),c_0_33]),c_0_89]),c_0_47]) ).

cnf(c_0_92,hypothesis,
    multiply(c,multiply(b,multiply(b,X1))) = multiply(c,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_90]),c_0_30]) ).

cnf(c_0_93,hypothesis,
    multiply(X1,multiply(X1,add(X1,X2))) = add(X1,multiply(X1,multiply(X1,X2))),
    inference(spm,[status(thm)],[c_0_57,c_0_16]) ).

cnf(c_0_94,hypothesis,
    multiply(c,add(c,additive_inverse(multiply(b,a)))) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_91]),c_0_33]),c_0_33]),c_0_92]) ).

cnf(c_0_95,hypothesis,
    add(c,additive_inverse(multiply(c,multiply(c,multiply(b,a))))) = additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_33]),c_0_47]),c_0_47]) ).

cnf(c_0_96,hypothesis,
    multiply(c,multiply(c,multiply(b,a))) = c,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_95]),c_0_73]),c_0_15]),c_0_19]) ).

cnf(c_0_97,hypothesis,
    multiply(a,multiply(c,multiply(b,a))) = multiply(b,multiply(b,a)),
    inference(spm,[status(thm)],[c_0_56,c_0_53]) ).

cnf(c_0_98,hypothesis,
    multiply(c,multiply(b,a)) = multiply(c,c),
    inference(spm,[status(thm)],[c_0_34,c_0_96]) ).

cnf(c_0_99,negated_conjecture,
    multiply(a,multiply(c,c)) = multiply(b,c),
    inference(spm,[status(thm)],[c_0_56,c_0_17]) ).

cnf(c_0_100,hypothesis,
    multiply(X1,add(X2,additive_inverse(multiply(X1,multiply(X1,X2))))) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_12]),c_0_33]) ).

cnf(c_0_101,hypothesis,
    multiply(b,multiply(b,a)) = multiply(b,c),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98]),c_0_99]) ).

cnf(c_0_102,hypothesis,
    multiply(b,multiply(a,c)) = multiply(a,multiply(c,b)),
    inference(spm,[status(thm)],[c_0_56,c_0_82]) ).

cnf(c_0_103,hypothesis,
    multiply(b,add(a,additive_inverse(multiply(b,c)))) = additive_identity,
    inference(spm,[status(thm)],[c_0_100,c_0_101]) ).

cnf(c_0_104,hypothesis,
    multiply(b,multiply(b,multiply(c,b))) = multiply(b,c),
    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(spm,[status(thm)],[c_0_45,c_0_101]),c_0_30]),c_0_55]),c_0_63]),c_0_102]),c_0_30]),c_0_64]) ).

cnf(c_0_105,hypothesis,
    multiply(b,multiply(b,c)) = multiply(b,a),
    inference(spm,[status(thm)],[c_0_34,c_0_101]) ).

cnf(c_0_106,hypothesis,
    multiply(b,multiply(add(a,additive_inverse(multiply(b,c))),X1)) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_103]),c_0_42]) ).

cnf(c_0_107,negated_conjecture,
    multiply(add(a,X1),b) = add(c,multiply(X1,b)),
    inference(spm,[status(thm)],[c_0_24,c_0_17]) ).

cnf(c_0_108,hypothesis,
    multiply(b,multiply(c,b)) = multiply(b,a),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_104]),c_0_105]) ).

cnf(c_0_109,hypothesis,
    add(c,additive_inverse(multiply(b,a))) = additive_identity,
    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_45,c_0_106]),c_0_33]),c_0_107]),c_0_51]),c_0_30]),c_0_108]) ).

cnf(c_0_110,negated_conjecture,
    multiply(b,a) != c,
    prove_commutativity ).

cnf(c_0_111,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_109]),c_0_73]),c_0_15]),c_0_19]),c_0_110]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : RNG009-7 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n010.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Sun Aug 27 02:48:49 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.85/0.97  % Version  : CSE_E---1.5
% 0.85/0.97  % Problem  : theBenchmark.p
% 0.85/0.97  % Proof found
% 0.85/0.97  % SZS status Theorem for theBenchmark.p
% 0.85/0.97  % SZS output start Proof
% See solution above
% 0.85/0.98  % Total time : 0.402000 s
% 0.85/0.98  % SZS output end Proof
% 0.85/0.98  % Total time : 0.405000 s
%------------------------------------------------------------------------------