TSTP Solution File: RNG004-10 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : RNG004-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 : Wed May 31 12:32:33 EDT 2023

% Result   : Unsatisfiable 72.72s 9.55s
% Output   : CNFRefutation 75.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   45
%            Number of leaves      :   16
% Syntax   : Number of formulae    :  147 ( 147 unt;   0 def)
%            Number of atoms       :  147 ( 146 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-4 aty)
%            Number of variables   :  251 (; 251   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B,C] : ifeq2(A,A,B,C) = B,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [A,B,C] : ifeq(A,A,B,C) = B,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X] : sum(additive_identity,X,X) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X] : sum(X,additive_identity,X) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X,Y] : product(X,Y,multiply(X,Y)) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X,Y] : sum(X,Y,add(X,Y)) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X] : sum(additive_inverse(X),X,additive_identity) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X] : sum(X,additive_inverse(X),additive_identity) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [U,Z,W,Y,V,X] : ifeq(sum(U,Z,W),true,ifeq(sum(Y,Z,V),true,ifeq(sum(X,Y,U),true,sum(X,V,W),true),true),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X,Y,Z] : ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [X,V3,V4,Z,V2,Y,V1] : ifeq(product(X,V3,V4),true,ifeq(product(X,Z,V2),true,ifeq(product(X,Y,V1),true,ifeq(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [V3,X,V4,Z,V2,Y,V1] : ifeq(product(V3,X,V4),true,ifeq(product(Z,X,V2),true,ifeq(product(Y,X,V1),true,ifeq(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [X,Y,V,U] : ifeq2(sum(X,Y,V),true,ifeq2(sum(X,Y,U),true,U,V),V) = V,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,hypothesis,
    product(a,b,c) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,hypothesis,
    product(additive_inverse(a),additive_inverse(b),d) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,negated_conjecture,
    c != d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,plain,
    ! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f24,plain,
    ! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f25,plain,
    ! [X0] : sum(additive_identity,X0,X0) = true,
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f26,plain,
    ! [X0] : sum(X0,additive_identity,X0) = true,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f27,plain,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f28,plain,
    ! [X0,X1] : sum(X0,X1,add(X0,X1)) = true,
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f29,plain,
    ! [X0] : sum(additive_inverse(X0),X0,additive_identity) = true,
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f30,plain,
    ! [X0] : sum(X0,additive_inverse(X0),additive_identity) = true,
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f31,plain,
    ! [X0,X1,X2,X3,X4,X5] : ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(sum(X5,X3,X0),true,sum(X5,X4,X2),true),true),true) = true,
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f33,plain,
    ! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f36,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true) = true,
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f38,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X1,X6),true,ifeq(sum(X5,X3,X0),true,sum(X6,X4,X2),true),true),true),true) = true,
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f40,plain,
    ! [X0,X1,X2,X3] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2,
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f42,plain,
    product(a,b,c) = true,
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f43,plain,
    product(additive_inverse(a),additive_inverse(b),d) = true,
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f44,plain,
    c != d,
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f53,plain,
    ! [X0,X1] : ifeq(true,true,sum(X0,X1,add(X1,X0)),true) = true,
    inference(paramodulation,[status(thm)],[f28,f33]) ).

fof(f54,plain,
    ! [X0,X1] : sum(X0,X1,add(X1,X0)) = true,
    inference(forward_demodulation,[status(thm)],[f24,f53]) ).

fof(f71,plain,
    ! [X0,X1] : ifeq2(true,true,ifeq2(sum(additive_identity,X0,X1),true,X1,X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f25,f40]) ).

fof(f72,plain,
    ! [X0,X1] : ifeq2(sum(additive_identity,X0,X1),true,X1,X0) = X0,
    inference(forward_demodulation,[status(thm)],[f23,f71]) ).

fof(f79,plain,
    ! [X0,X1,X2] : ifeq2(true,true,ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)),add(X0,X1)) = add(X0,X1),
    inference(paramodulation,[status(thm)],[f28,f40]) ).

fof(f80,plain,
    ! [X0,X1,X2] : ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)) = add(X0,X1),
    inference(forward_demodulation,[status(thm)],[f23,f79]) ).

fof(f81,plain,
    ! [X0,X1] : ifeq2(sum(additive_inverse(X0),X0,X1),true,ifeq2(true,true,additive_identity,X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f29,f40]) ).

fof(f82,plain,
    ! [X0,X1] : ifeq2(sum(additive_inverse(X0),X0,X1),true,additive_identity,X1) = X1,
    inference(forward_demodulation,[status(thm)],[f23,f81]) ).

fof(f87,plain,
    ! [X0,X1] : ifeq2(sum(X0,additive_identity,X1),true,ifeq2(true,true,X0,X1),X1) = X1,
    inference(paramodulation,[status(thm)],[f26,f40]) ).

fof(f88,plain,
    ! [X0,X1] : ifeq2(sum(X0,additive_identity,X1),true,X0,X1) = X1,
    inference(forward_demodulation,[status(thm)],[f23,f87]) ).

fof(f89,plain,
    ! [X0,X1,X2] : ifeq2(sum(X0,X1,X2),true,ifeq2(true,true,add(X1,X0),X2),X2) = X2,
    inference(paramodulation,[status(thm)],[f54,f40]) ).

fof(f90,plain,
    ! [X0,X1,X2] : ifeq2(sum(X0,X1,X2),true,add(X1,X0),X2) = X2,
    inference(forward_demodulation,[status(thm)],[f23,f89]) ).

fof(f94,plain,
    ifeq2(true,true,additive_identity,additive_inverse(additive_identity)) = additive_inverse(additive_identity),
    inference(paramodulation,[status(thm)],[f30,f72]) ).

fof(f95,plain,
    additive_identity = additive_inverse(additive_identity),
    inference(forward_demodulation,[status(thm)],[f23,f94]) ).

fof(f99,plain,
    ! [X0] : ifeq2(true,true,add(additive_identity,X0),X0) = X0,
    inference(paramodulation,[status(thm)],[f28,f72]) ).

fof(f100,plain,
    ! [X0] : add(additive_identity,X0) = X0,
    inference(forward_demodulation,[status(thm)],[f23,f99]) ).

fof(f104,plain,
    ! [X0,X1,X2,X3] : ifeq(true,true,ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,additive_identity),true,sum(X3,X2,X1),true),true),true) = true,
    inference(paramodulation,[status(thm)],[f25,f31]) ).

fof(f105,plain,
    ! [X0,X1,X2,X3] : ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,additive_identity),true,sum(X3,X2,X1),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f104]) ).

fof(f224,plain,
    ! [X0] : ifeq2(true,true,additive_identity,add(X0,additive_inverse(X0))) = add(X0,additive_inverse(X0)),
    inference(paramodulation,[status(thm)],[f54,f82]) ).

fof(f225,plain,
    ! [X0] : additive_identity = add(X0,additive_inverse(X0)),
    inference(forward_demodulation,[status(thm)],[f23,f224]) ).

fof(f226,plain,
    ! [X0] : ifeq2(true,true,additive_identity,add(additive_inverse(X0),X0)) = add(additive_inverse(X0),X0),
    inference(paramodulation,[status(thm)],[f28,f82]) ).

fof(f227,plain,
    ! [X0] : additive_identity = add(additive_inverse(X0),X0),
    inference(forward_demodulation,[status(thm)],[f23,f226]) ).

fof(f258,plain,
    ! [X0,X1] : ifeq2(true,true,add(X0,X1),add(X1,X0)) = add(X1,X0),
    inference(paramodulation,[status(thm)],[f28,f90]) ).

fof(f259,plain,
    ! [X0,X1] : add(X0,X1) = add(X1,X0),
    inference(forward_demodulation,[status(thm)],[f23,f258]) ).

fof(f343,plain,
    ! [X0,X1,X2,X3] : ifeq(true,true,ifeq(product(additive_inverse(a),X0,X1),true,ifeq(product(additive_inverse(a),X2,X3),true,ifeq(sum(X2,X0,additive_inverse(b)),true,sum(X3,X1,d),true),true),true),true) = true,
    inference(paramodulation,[status(thm)],[f43,f36]) ).

fof(f344,plain,
    ! [X0,X1,X2,X3] : ifeq(product(additive_inverse(a),X0,X1),true,ifeq(product(additive_inverse(a),X2,X3),true,ifeq(sum(X2,X0,additive_inverse(b)),true,sum(X3,X1,d),true),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f343]) ).

fof(f349,plain,
    ! [X0,X1,X2,X3] : ifeq(product(additive_inverse(a),X0,X1),true,ifeq(true,true,ifeq(product(additive_inverse(a),X2,X3),true,ifeq(sum(X2,additive_inverse(b),X0),true,sum(X3,d,X1),true),true),true),true) = true,
    inference(paramodulation,[status(thm)],[f43,f36]) ).

fof(f350,plain,
    ! [X0,X1,X2,X3] : ifeq(product(additive_inverse(a),X0,X1),true,ifeq(product(additive_inverse(a),X2,X3),true,ifeq(sum(X2,additive_inverse(b),X0),true,sum(X3,d,X1),true),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f349]) ).

fof(f701,plain,
    ! [X0,X1,X2,X3] : ifeq(true,true,ifeq(product(X0,b,X1),true,ifeq(product(X2,b,X3),true,ifeq(sum(X2,X0,a),true,sum(X3,X1,c),true),true),true),true) = true,
    inference(paramodulation,[status(thm)],[f42,f38]) ).

fof(f702,plain,
    ! [X0,X1,X2,X3] : ifeq(product(X0,b,X1),true,ifeq(product(X2,b,X3),true,ifeq(sum(X2,X0,a),true,sum(X3,X1,c),true),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f701]) ).

fof(f709,plain,
    ! [X0,X1,X2,X3] : ifeq(product(X0,b,X1),true,ifeq(true,true,ifeq(product(X2,b,X3),true,ifeq(sum(X2,a,X0),true,sum(X3,c,X1),true),true),true),true) = true,
    inference(paramodulation,[status(thm)],[f42,f38]) ).

fof(f710,plain,
    ! [X0,X1,X2,X3] : ifeq(product(X0,b,X1),true,ifeq(product(X2,b,X3),true,ifeq(sum(X2,a,X0),true,sum(X3,c,X1),true),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f709]) ).

fof(f1033,plain,
    ! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,ifeq(true,true,sum(additive_inverse(X0),X2,X1),true),true) = true,
    inference(paramodulation,[status(thm)],[f29,f105]) ).

fof(f1034,plain,
    ! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,sum(additive_inverse(X0),X2,X1),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f1033]) ).

fof(f1037,plain,
    ! [X0,X1,X2] : ifeq(sum(additive_inverse(X0),X1,X2),true,ifeq(true,true,sum(X0,X2,X1),true),true) = true,
    inference(paramodulation,[status(thm)],[f30,f105]) ).

fof(f1038,plain,
    ! [X0,X1,X2] : ifeq(sum(additive_inverse(X0),X1,X2),true,sum(X0,X2,X1),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f1037]) ).

fof(f1384,plain,
    ! [X0] : ifeq(true,true,sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),true) = true,
    inference(paramodulation,[status(thm)],[f29,f1034]) ).

fof(f1385,plain,
    ! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0) = true,
    inference(forward_demodulation,[status(thm)],[f24,f1384]) ).

fof(f1393,plain,
    ! [X0,X1] : ifeq(true,true,sum(additive_inverse(X0),add(X1,X0),X1),true) = true,
    inference(paramodulation,[status(thm)],[f54,f1034]) ).

fof(f1394,plain,
    ! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1) = true,
    inference(forward_demodulation,[status(thm)],[f24,f1393]) ).

fof(f1415,plain,
    ! [X0] : ifeq2(true,true,additive_inverse(additive_inverse(X0)),X0) = X0,
    inference(paramodulation,[status(thm)],[f1385,f88]) ).

fof(f1416,plain,
    ! [X0] : additive_inverse(additive_inverse(X0)) = X0,
    inference(forward_demodulation,[status(thm)],[f23,f1415]) ).

fof(f1797,plain,
    ! [X0,X1] : ifeq2(true,true,X0,add(additive_inverse(X1),add(X0,X1))) = add(additive_inverse(X1),add(X0,X1)),
    inference(paramodulation,[status(thm)],[f1394,f80]) ).

fof(f1798,plain,
    ! [X0,X1] : X0 = add(additive_inverse(X1),add(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f23,f1797]) ).

fof(f1831,plain,
    ! [X0,X1] : X0 = add(X1,add(X0,additive_inverse(X1))),
    inference(paramodulation,[status(thm)],[f1416,f1798]) ).

fof(f1834,plain,
    ! [X0,X1] : additive_inverse(X0) = add(additive_inverse(add(X1,X0)),X1),
    inference(paramodulation,[status(thm)],[f1798,f1798]) ).

fof(f1835,plain,
    ! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X1,X0))),
    inference(forward_demodulation,[status(thm)],[f259,f1834]) ).

fof(f1842,plain,
    ! [X0,X1] : X0 = add(additive_inverse(X1),add(X1,X0)),
    inference(paramodulation,[status(thm)],[f259,f1798]) ).

fof(f1864,plain,
    ! [X0,X1] : X0 = add(X1,add(additive_inverse(X1),X0)),
    inference(paramodulation,[status(thm)],[f259,f1831]) ).

fof(f1904,plain,
    ! [X0,X1] : additive_inverse(X0) = add(additive_inverse(add(X0,X1)),X1),
    inference(paramodulation,[status(thm)],[f1842,f1798]) ).

fof(f1905,plain,
    ! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f259,f1904]) ).

fof(f1953,plain,
    ! [X0,X1] : sum(add(additive_inverse(X0),X1),X0,X1) = true,
    inference(paramodulation,[status(thm)],[f1864,f54]) ).

fof(f2160,plain,
    ! [X0,X1] : ifeq(true,true,ifeq(product(additive_inverse(a),X0,X1),true,ifeq(sum(X0,additive_inverse(b),additive_inverse(b)),true,sum(X1,d,d),true),true),true) = true,
    inference(paramodulation,[status(thm)],[f43,f344]) ).

fof(f2161,plain,
    ! [X0,X1] : ifeq(product(additive_inverse(a),X0,X1),true,ifeq(sum(X0,additive_inverse(b),additive_inverse(b)),true,sum(X1,d,d),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f2160]) ).

fof(f2542,plain,
    ! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X0),additive_inverse(X1)),
    inference(paramodulation,[status(thm)],[f1842,f1835]) ).

fof(f2547,plain,
    ! [X0,X1] : additive_inverse(add(additive_inverse(X0),X1)) = add(X0,additive_inverse(X1)),
    inference(paramodulation,[status(thm)],[f1864,f1835]) ).

fof(f3196,plain,
    ! [X0,X1] : ifeq(product(additive_inverse(a),additive_identity,X0),true,ifeq(product(additive_inverse(a),additive_inverse(additive_inverse(b)),X1),true,ifeq(true,true,sum(X1,d,X0),true),true),true) = true,
    inference(paramodulation,[status(thm)],[f29,f350]) ).

fof(f3197,plain,
    ! [X0,X1] : ifeq(product(additive_inverse(a),additive_identity,X0),true,ifeq(product(additive_inverse(a),b,X1),true,ifeq(true,true,sum(X1,d,X0),true),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f1416,f3196]) ).

fof(f3198,plain,
    ! [X0,X1] : ifeq(product(additive_inverse(a),additive_identity,X0),true,ifeq(product(additive_inverse(a),b,X1),true,sum(X1,d,X0),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f3197]) ).

fof(f6081,plain,
    ! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X1),additive_inverse(X0)),
    inference(paramodulation,[status(thm)],[f259,f2542]) ).

fof(f6082,plain,
    ! [X0,X1] : additive_inverse(add(X0,X1)) = additive_inverse(add(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f2542,f6081]) ).

fof(f6215,plain,
    ! [X0,X1,X2] : X0 = add(add(X1,X2),add(additive_inverse(add(X2,X1)),X0)),
    inference(paramodulation,[status(thm)],[f6082,f1864]) ).

fof(f6233,plain,
    ! [X0,X1] : additive_identity = add(additive_inverse(add(X0,X1)),add(X1,X0)),
    inference(paramodulation,[status(thm)],[f6082,f227]) ).

fof(f6234,plain,
    ! [X0,X1] : additive_identity = add(add(X0,X1),additive_inverse(add(X1,X0))),
    inference(forward_demodulation,[status(thm)],[f259,f6233]) ).

fof(f7425,plain,
    ! [X0,X1] : ifeq(true,true,ifeq(product(X0,b,X1),true,ifeq(sum(X0,a,a),true,sum(X1,c,c),true),true),true) = true,
    inference(paramodulation,[status(thm)],[f42,f702]) ).

fof(f7426,plain,
    ! [X0,X1] : ifeq(product(X0,b,X1),true,ifeq(sum(X0,a,a),true,sum(X1,c,c),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f7425]) ).

fof(f7579,plain,
    ! [X0,X1,X2] : ifeq(true,true,ifeq(product(X0,b,X1),true,ifeq(sum(X0,a,X2),true,sum(X1,c,multiply(X2,b)),true),true),true) = true,
    inference(paramodulation,[status(thm)],[f27,f710]) ).

fof(f7580,plain,
    ! [X0,X1,X2] : ifeq(product(X0,b,X1),true,ifeq(sum(X0,a,X2),true,sum(X1,c,multiply(X2,b)),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f7579]) ).

fof(f10316,plain,
    ! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X2,X1),X0),
    inference(paramodulation,[status(thm)],[f1798,f6215]) ).

fof(f17447,plain,
    ! [X0] : ifeq(product(additive_inverse(a),add(additive_inverse(additive_inverse(b)),additive_inverse(b)),X0),true,ifeq(true,true,sum(X0,d,d),true),true) = true,
    inference(paramodulation,[status(thm)],[f1953,f2161]) ).

fof(f17448,plain,
    ! [X0] : ifeq(product(additive_inverse(a),additive_inverse(add(additive_inverse(b),b)),X0),true,ifeq(true,true,sum(X0,d,d),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f2542,f17447]) ).

fof(f17449,plain,
    ! [X0] : ifeq(product(additive_inverse(a),add(b,additive_inverse(b)),X0),true,ifeq(true,true,sum(X0,d,d),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f2547,f17448]) ).

fof(f17450,plain,
    ! [X0] : ifeq(product(additive_inverse(a),additive_identity,X0),true,ifeq(true,true,sum(X0,d,d),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f225,f17449]) ).

fof(f17451,plain,
    ! [X0] : ifeq(product(additive_inverse(a),additive_identity,X0),true,sum(X0,d,d),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f17450]) ).

fof(f22762,plain,
    ifeq(true,true,sum(multiply(additive_inverse(a),additive_identity),d,d),true) = true,
    inference(paramodulation,[status(thm)],[f27,f17451]) ).

fof(f22763,plain,
    sum(multiply(additive_inverse(a),additive_identity),d,d) = true,
    inference(forward_demodulation,[status(thm)],[f24,f22762]) ).

fof(f23003,plain,
    ifeq2(true,true,d,add(multiply(additive_inverse(a),additive_identity),d)) = add(multiply(additive_inverse(a),additive_identity),d),
    inference(paramodulation,[status(thm)],[f22763,f80]) ).

fof(f23004,plain,
    d = add(multiply(additive_inverse(a),additive_identity),d),
    inference(forward_demodulation,[status(thm)],[f23,f23003]) ).

fof(f23005,plain,
    d = add(d,multiply(additive_inverse(a),additive_identity)),
    inference(forward_demodulation,[status(thm)],[f259,f23004]) ).

fof(f23133,plain,
    additive_identity = add(add(multiply(additive_inverse(a),additive_identity),d),additive_inverse(d)),
    inference(paramodulation,[status(thm)],[f23005,f6234]) ).

fof(f23134,plain,
    additive_identity = add(additive_inverse(d),add(d,multiply(additive_inverse(a),additive_identity))),
    inference(forward_demodulation,[status(thm)],[f10316,f23133]) ).

fof(f23135,plain,
    additive_identity = multiply(additive_inverse(a),additive_identity),
    inference(forward_demodulation,[status(thm)],[f1842,f23134]) ).

fof(f23202,plain,
    product(additive_inverse(a),additive_identity,additive_identity) = true,
    inference(paramodulation,[status(thm)],[f23135,f27]) ).

fof(f23209,plain,
    ! [X0] : ifeq(true,true,ifeq(product(additive_inverse(a),b,X0),true,sum(X0,d,additive_identity),true),true) = true,
    inference(paramodulation,[status(thm)],[f23202,f3198]) ).

fof(f23210,plain,
    ! [X0] : ifeq(product(additive_inverse(a),b,X0),true,sum(X0,d,additive_identity),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f23209]) ).

fof(f64444,plain,
    ifeq(true,true,sum(multiply(additive_inverse(a),b),d,additive_identity),true) = true,
    inference(paramodulation,[status(thm)],[f27,f23210]) ).

fof(f64445,plain,
    sum(multiply(additive_inverse(a),b),d,additive_identity) = true,
    inference(forward_demodulation,[status(thm)],[f24,f64444]) ).

fof(f64835,plain,
    ifeq2(true,true,additive_identity,add(multiply(additive_inverse(a),b),d)) = add(multiply(additive_inverse(a),b),d),
    inference(paramodulation,[status(thm)],[f64445,f80]) ).

fof(f64836,plain,
    additive_identity = add(multiply(additive_inverse(a),b),d),
    inference(forward_demodulation,[status(thm)],[f23,f64835]) ).

fof(f64837,plain,
    additive_identity = add(d,multiply(additive_inverse(a),b)),
    inference(forward_demodulation,[status(thm)],[f259,f64836]) ).

fof(f65198,plain,
    additive_inverse(d) = add(multiply(additive_inverse(a),b),additive_inverse(additive_identity)),
    inference(paramodulation,[status(thm)],[f64837,f1905]) ).

fof(f65199,plain,
    additive_inverse(d) = add(additive_inverse(additive_identity),multiply(additive_inverse(a),b)),
    inference(forward_demodulation,[status(thm)],[f259,f65198]) ).

fof(f65200,plain,
    additive_inverse(d) = add(additive_identity,multiply(additive_inverse(a),b)),
    inference(forward_demodulation,[status(thm)],[f95,f65199]) ).

fof(f65201,plain,
    additive_inverse(d) = multiply(additive_inverse(a),b),
    inference(forward_demodulation,[status(thm)],[f100,f65200]) ).

fof(f65281,plain,
    product(additive_inverse(a),b,additive_inverse(d)) = true,
    inference(paramodulation,[status(thm)],[f65201,f27]) ).

fof(f98534,plain,
    ! [X0] : ifeq(product(add(additive_inverse(a),a),b,X0),true,ifeq(true,true,sum(X0,c,c),true),true) = true,
    inference(paramodulation,[status(thm)],[f1953,f7426]) ).

fof(f98535,plain,
    ! [X0] : ifeq(product(additive_identity,b,X0),true,ifeq(true,true,sum(X0,c,c),true),true) = true,
    inference(forward_demodulation,[status(thm)],[f227,f98534]) ).

fof(f98536,plain,
    ! [X0] : ifeq(product(additive_identity,b,X0),true,sum(X0,c,c),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f98535]) ).

fof(f98555,plain,
    ifeq(true,true,sum(multiply(additive_identity,b),c,c),true) = true,
    inference(paramodulation,[status(thm)],[f27,f98536]) ).

fof(f98556,plain,
    sum(multiply(additive_identity,b),c,c) = true,
    inference(forward_demodulation,[status(thm)],[f24,f98555]) ).

fof(f98942,plain,
    ifeq2(true,true,c,add(multiply(additive_identity,b),c)) = add(multiply(additive_identity,b),c),
    inference(paramodulation,[status(thm)],[f98556,f80]) ).

fof(f98943,plain,
    c = add(multiply(additive_identity,b),c),
    inference(forward_demodulation,[status(thm)],[f23,f98942]) ).

fof(f98944,plain,
    c = add(c,multiply(additive_identity,b)),
    inference(forward_demodulation,[status(thm)],[f259,f98943]) ).

fof(f99222,plain,
    multiply(additive_identity,b) = add(additive_inverse(c),c),
    inference(paramodulation,[status(thm)],[f98944,f1842]) ).

fof(f99223,plain,
    multiply(additive_identity,b) = additive_identity,
    inference(forward_demodulation,[status(thm)],[f227,f99222]) ).

fof(f103214,plain,
    ! [X0] : ifeq(product(additive_inverse(a),b,X0),true,ifeq(true,true,sum(X0,c,multiply(additive_identity,b)),true),true) = true,
    inference(paramodulation,[status(thm)],[f29,f7580]) ).

fof(f103215,plain,
    ! [X0] : ifeq(product(additive_inverse(a),b,X0),true,sum(X0,c,multiply(additive_identity,b)),true) = true,
    inference(forward_demodulation,[status(thm)],[f24,f103214]) ).

fof(f103216,plain,
    ! [X0] : ifeq(product(additive_inverse(a),b,X0),true,sum(X0,c,additive_identity),true) = true,
    inference(forward_demodulation,[status(thm)],[f99223,f103215]) ).

fof(f174480,plain,
    ifeq(true,true,sum(additive_inverse(d),c,additive_identity),true) = true,
    inference(paramodulation,[status(thm)],[f65281,f103216]) ).

fof(f174481,plain,
    sum(additive_inverse(d),c,additive_identity) = true,
    inference(forward_demodulation,[status(thm)],[f24,f174480]) ).

fof(f174521,plain,
    ifeq(true,true,sum(d,additive_identity,c),true) = true,
    inference(paramodulation,[status(thm)],[f174481,f1038]) ).

fof(f174522,plain,
    sum(d,additive_identity,c) = true,
    inference(forward_demodulation,[status(thm)],[f24,f174521]) ).

fof(f175113,plain,
    ifeq2(true,true,d,c) = c,
    inference(paramodulation,[status(thm)],[f174522,f88]) ).

fof(f175114,plain,
    d = c,
    inference(forward_demodulation,[status(thm)],[f23,f175113]) ).

fof(f175115,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f175114,f44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : RNG004-10 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n019.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 : Tue May 30 10:36:10 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Drodi V3.5.1
% 72.72/9.55  % Refutation found
% 72.72/9.55  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 72.72/9.55  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 75.53/9.94  % Elapsed time: 9.565628 seconds
% 75.53/9.94  % CPU time: 74.523141 seconds
% 75.53/9.94  % Memory used: 755.094 MB
%------------------------------------------------------------------------------