TSTP Solution File: RNG009-7 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : RNG009-7 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n005.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 : Tue May 21 02:40:28 EDT 2024

% Result   : Unsatisfiable 51.26s 7.71s
% Output   : Refutation 51.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   44
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  191 ( 191 unt;   0 def)
%            Number of atoms       :  191 ( 190 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    1 (   1   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            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   :  170 ( 170   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f153899,plain,
    $false,
    inference(subsumption_resolution,[],[f153898,f12]) ).

fof(f12,axiom,
    c != multiply(b,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).

fof(f153898,plain,
    c = multiply(b,a),
    inference(forward_demodulation,[],[f153840,f938]) ).

fof(f938,plain,
    c = multiply(a,multiply(a,c)),
    inference(superposition,[],[f77,f11]) ).

fof(f11,axiom,
    multiply(a,b) = c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).

fof(f77,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X0,multiply(X0,X1))),
    inference(forward_demodulation,[],[f72,f7]) ).

fof(f7,axiom,
    ! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_multiplication) ).

fof(f72,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(multiply(X0,X0),X1)),
    inference(superposition,[],[f7,f10]) ).

fof(f10,axiom,
    ! [X0] : multiply(X0,multiply(X0,X0)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_x) ).

fof(f153840,plain,
    multiply(b,a) = multiply(a,multiply(a,c)),
    inference(superposition,[],[f143191,f153693]) ).

fof(f153693,plain,
    multiply(a,c) = multiply(c,a),
    inference(superposition,[],[f153554,f71]) ).

fof(f71,plain,
    ! [X0] : multiply(a,multiply(b,X0)) = multiply(c,X0),
    inference(superposition,[],[f7,f11]) ).

fof(f153554,plain,
    multiply(a,c) = multiply(a,multiply(b,a)),
    inference(forward_demodulation,[],[f153553,f144056]) ).

fof(f144056,plain,
    multiply(b,a) = multiply(b,multiply(c,b)),
    inference(forward_demodulation,[],[f144055,f122331]) ).

fof(f122331,plain,
    ! [X0,X1] : multiply(X0,X1) = additive_inverse(multiply(X0,additive_inverse(X1))),
    inference(superposition,[],[f63,f121719]) ).

fof(f121719,plain,
    ! [X0,X1] : multiply(X1,additive_inverse(X0)) = additive_inverse(multiply(X1,X0)),
    inference(forward_demodulation,[],[f121718,f6689]) ).

fof(f6689,plain,
    ! [X0] : additive_inverse(X0) = multiply(additive_inverse(X0),multiply(X0,X0)),
    inference(forward_demodulation,[],[f6634,f2]) ).

fof(f2,axiom,
    ! [X0] : add(X0,additive_identity) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_identity) ).

fof(f6634,plain,
    ! [X0] : add(additive_inverse(X0),additive_identity) = multiply(additive_inverse(X0),multiply(X0,X0)),
    inference(superposition,[],[f49,f6529]) ).

fof(f6529,plain,
    ! [X0] : additive_identity = add(X0,multiply(additive_inverse(X0),multiply(X0,X0))),
    inference(forward_demodulation,[],[f6528,f5232]) ).

fof(f5232,plain,
    ! [X0] : additive_identity = multiply(additive_identity,X0),
    inference(forward_demodulation,[],[f5215,f3]) ).

fof(f3,axiom,
    ! [X0] : additive_identity = add(additive_inverse(X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_inverse) ).

fof(f5215,plain,
    ! [X0] : multiply(additive_identity,X0) = add(additive_inverse(multiply(additive_identity,X0)),multiply(additive_identity,X0)),
    inference(superposition,[],[f49,f5055]) ).

fof(f5055,plain,
    ! [X0] : multiply(additive_identity,X0) = add(multiply(additive_identity,X0),multiply(additive_identity,X0)),
    inference(forward_demodulation,[],[f5054,f3720]) ).

fof(f3720,plain,
    ! [X0,X1] : multiply(additive_identity,X1) = multiply(X0,multiply(additive_identity,X1)),
    inference(superposition,[],[f7,f3650]) ).

fof(f3650,plain,
    ! [X0] : additive_identity = multiply(X0,additive_identity),
    inference(forward_demodulation,[],[f3615,f3]) ).

fof(f3615,plain,
    ! [X0] : add(additive_inverse(X0),X0) = multiply(X0,additive_identity),
    inference(superposition,[],[f49,f3514]) ).

fof(f3514,plain,
    ! [X0] : add(X0,multiply(X0,additive_identity)) = X0,
    inference(forward_demodulation,[],[f3464,f10]) ).

fof(f3464,plain,
    ! [X0] : multiply(X0,multiply(X0,X0)) = add(X0,multiply(X0,additive_identity)),
    inference(superposition,[],[f154,f2]) ).

fof(f154,plain,
    ! [X0,X1] : multiply(X0,add(multiply(X0,X0),X1)) = add(X0,multiply(X0,X1)),
    inference(superposition,[],[f8,f10]) ).

fof(f8,axiom,
    ! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).

fof(f5054,plain,
    ! [X0,X1] : multiply(additive_identity,X0) = add(multiply(additive_identity,X0),multiply(X1,multiply(additive_identity,X0))),
    inference(forward_demodulation,[],[f4852,f3720]) ).

fof(f4852,plain,
    ! [X0,X1] : add(multiply(additive_identity,X0),multiply(X1,multiply(additive_identity,X0))) = multiply(add(X1,additive_inverse(c)),multiply(additive_identity,X0)),
    inference(superposition,[],[f259,f3697]) ).

fof(f3697,plain,
    ! [X0] : multiply(additive_identity,X0) = multiply(additive_inverse(c),multiply(additive_identity,X0)),
    inference(superposition,[],[f7,f3667]) ).

fof(f3667,plain,
    additive_identity = multiply(additive_inverse(c),additive_identity),
    inference(forward_demodulation,[],[f3666,f211]) ).

fof(f211,plain,
    additive_identity = add(c,multiply(a,additive_inverse(b))),
    inference(forward_demodulation,[],[f187,f197]) ).

fof(f197,plain,
    additive_identity = multiply(a,additive_identity),
    inference(forward_demodulation,[],[f195,f3]) ).

fof(f195,plain,
    multiply(a,additive_identity) = add(additive_inverse(c),c),
    inference(superposition,[],[f49,f191]) ).

fof(f191,plain,
    c = add(c,multiply(a,additive_identity)),
    inference(forward_demodulation,[],[f184,f11]) ).

fof(f184,plain,
    multiply(a,b) = add(c,multiply(a,additive_identity)),
    inference(superposition,[],[f156,f2]) ).

fof(f156,plain,
    ! [X0] : multiply(a,add(b,X0)) = add(c,multiply(a,X0)),
    inference(superposition,[],[f8,f11]) ).

fof(f187,plain,
    multiply(a,additive_identity) = add(c,multiply(a,additive_inverse(b))),
    inference(superposition,[],[f156,f4]) ).

fof(f4,axiom,
    ! [X0] : additive_identity = add(X0,additive_inverse(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_inverse) ).

fof(f3666,plain,
    add(c,multiply(a,additive_inverse(b))) = multiply(additive_inverse(c),additive_identity),
    inference(forward_demodulation,[],[f3635,f220]) ).

fof(f220,plain,
    ! [X0] : multiply(a,multiply(additive_inverse(b),X0)) = multiply(additive_inverse(c),X0),
    inference(superposition,[],[f7,f215]) ).

fof(f215,plain,
    multiply(a,additive_inverse(b)) = additive_inverse(c),
    inference(forward_demodulation,[],[f213,f2]) ).

fof(f213,plain,
    multiply(a,additive_inverse(b)) = add(additive_inverse(c),additive_identity),
    inference(superposition,[],[f49,f211]) ).

fof(f3635,plain,
    add(c,multiply(a,additive_inverse(b))) = multiply(a,multiply(additive_inverse(b),additive_identity)),
    inference(superposition,[],[f185,f3514]) ).

fof(f185,plain,
    ! [X0] : multiply(a,X0) = add(c,multiply(a,add(additive_inverse(b),X0))),
    inference(superposition,[],[f156,f46]) ).

fof(f46,plain,
    ! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
    inference(forward_demodulation,[],[f32,f1]) ).

fof(f1,axiom,
    ! [X0] : add(additive_identity,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_identity) ).

fof(f32,plain,
    ! [X0,X1] : add(additive_identity,X1) = add(X0,add(additive_inverse(X0),X1)),
    inference(superposition,[],[f5,f4]) ).

fof(f5,axiom,
    ! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).

fof(f259,plain,
    ! [X2,X0,X1] : multiply(add(X0,X2),X1) = add(multiply(X2,X1),multiply(X0,X1)),
    inference(superposition,[],[f9,f6]) ).

fof(f6,axiom,
    ! [X0,X1] : add(X0,X1) = add(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).

fof(f9,axiom,
    ! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).

fof(f6528,plain,
    ! [X0] : multiply(additive_identity,multiply(X0,X0)) = add(X0,multiply(additive_inverse(X0),multiply(X0,X0))),
    inference(forward_demodulation,[],[f6460,f686]) ).

fof(f686,plain,
    ! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X0,X1))),
    inference(forward_demodulation,[],[f643,f2]) ).

fof(f643,plain,
    ! [X0,X1] : add(X1,additive_inverse(add(X0,X1))) = add(additive_inverse(X0),additive_identity),
    inference(superposition,[],[f49,f39]) ).

fof(f39,plain,
    ! [X0,X1] : additive_identity = add(X0,add(X1,additive_inverse(add(X0,X1)))),
    inference(superposition,[],[f5,f4]) ).

fof(f6460,plain,
    ! [X0,X1] : multiply(additive_identity,multiply(X0,X0)) = add(X0,multiply(add(X1,additive_inverse(add(X0,X1))),multiply(X0,X0))),
    inference(superposition,[],[f236,f39]) ).

fof(f236,plain,
    ! [X0,X1] : multiply(add(X0,X1),multiply(X0,X0)) = add(X0,multiply(X1,multiply(X0,X0))),
    inference(superposition,[],[f9,f10]) ).

fof(f49,plain,
    ! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
    inference(forward_demodulation,[],[f37,f1]) ).

fof(f37,plain,
    ! [X0,X1] : add(additive_identity,X1) = add(additive_inverse(X0),add(X0,X1)),
    inference(superposition,[],[f5,f3]) ).

fof(f121718,plain,
    ! [X0,X1] : multiply(X1,multiply(additive_inverse(X0),multiply(X0,X0))) = additive_inverse(multiply(X1,X0)),
    inference(forward_demodulation,[],[f121717,f2]) ).

fof(f121717,plain,
    ! [X0,X1] : multiply(X1,multiply(additive_inverse(X0),multiply(X0,X0))) = add(additive_inverse(multiply(X1,X0)),additive_identity),
    inference(forward_demodulation,[],[f120903,f3650]) ).

fof(f120903,plain,
    ! [X0,X1] : multiply(X1,multiply(additive_inverse(X0),multiply(X0,X0))) = add(additive_inverse(multiply(X1,X0)),multiply(X1,additive_identity)),
    inference(superposition,[],[f169,f6529]) ).

fof(f169,plain,
    ! [X2,X0,X1] : multiply(X0,X2) = add(additive_inverse(multiply(X0,X1)),multiply(X0,add(X1,X2))),
    inference(superposition,[],[f49,f8]) ).

fof(f63,plain,
    ! [X0] : additive_inverse(additive_inverse(X0)) = X0,
    inference(forward_demodulation,[],[f56,f2]) ).

fof(f56,plain,
    ! [X0] : add(X0,additive_identity) = additive_inverse(additive_inverse(X0)),
    inference(superposition,[],[f46,f4]) ).

fof(f144055,plain,
    multiply(b,multiply(c,b)) = additive_inverse(multiply(b,additive_inverse(a))),
    inference(forward_demodulation,[],[f143984,f122331]) ).

fof(f143984,plain,
    additive_inverse(multiply(b,additive_inverse(a))) = multiply(b,additive_inverse(multiply(c,additive_inverse(b)))),
    inference(superposition,[],[f121719,f142472]) ).

fof(f142472,plain,
    multiply(b,additive_inverse(a)) = multiply(b,multiply(c,additive_inverse(b))),
    inference(forward_demodulation,[],[f121907,f121719]) ).

fof(f121907,plain,
    additive_inverse(multiply(b,a)) = multiply(b,multiply(c,additive_inverse(b))),
    inference(forward_demodulation,[],[f121174,f2]) ).

fof(f121174,plain,
    multiply(b,multiply(c,additive_inverse(b))) = add(additive_inverse(multiply(b,a)),additive_identity),
    inference(superposition,[],[f169,f27436]) ).

fof(f27436,plain,
    additive_identity = multiply(b,add(a,multiply(c,additive_inverse(b)))),
    inference(forward_demodulation,[],[f27435,f3650]) ).

fof(f27435,plain,
    multiply(b,additive_identity) = multiply(b,add(a,multiply(c,additive_inverse(b)))),
    inference(forward_demodulation,[],[f27401,f24409]) ).

fof(f24409,plain,
    ! [X0] : additive_identity = multiply(add(a,multiply(c,additive_inverse(b))),multiply(b,X0)),
    inference(forward_demodulation,[],[f24408,f5232]) ).

fof(f24408,plain,
    ! [X0] : multiply(additive_identity,X0) = multiply(add(a,multiply(c,additive_inverse(b))),multiply(b,X0)),
    inference(forward_demodulation,[],[f24292,f22043]) ).

fof(f22043,plain,
    multiply(c,additive_inverse(b)) = additive_inverse(multiply(c,b)),
    inference(forward_demodulation,[],[f22042,f1]) ).

fof(f22042,plain,
    additive_inverse(multiply(c,b)) = add(additive_identity,multiply(c,additive_inverse(b))),
    inference(forward_demodulation,[],[f22004,f13]) ).

fof(f13,plain,
    additive_identity = additive_inverse(additive_identity),
    inference(superposition,[],[f3,f2]) ).

fof(f22004,plain,
    additive_inverse(multiply(c,b)) = add(additive_inverse(additive_identity),multiply(c,additive_inverse(b))),
    inference(superposition,[],[f138,f21937]) ).

fof(f21937,plain,
    additive_identity = add(multiply(c,b),multiply(c,additive_inverse(b))),
    inference(forward_demodulation,[],[f21936,f197]) ).

fof(f21936,plain,
    multiply(a,additive_identity) = add(multiply(c,b),multiply(c,additive_inverse(b))),
    inference(forward_demodulation,[],[f21848,f71]) ).

fof(f21848,plain,
    multiply(a,additive_identity) = add(multiply(c,b),multiply(a,multiply(b,additive_inverse(b)))),
    inference(superposition,[],[f157,f12890]) ).

fof(f12890,plain,
    ! [X0] : additive_identity = add(multiply(X0,X0),multiply(X0,additive_inverse(X0))),
    inference(forward_demodulation,[],[f12889,f11328]) ).

fof(f11328,plain,
    ! [X0] : additive_inverse(X0) = multiply(X0,additive_inverse(multiply(X0,X0))),
    inference(forward_demodulation,[],[f11272,f2]) ).

fof(f11272,plain,
    ! [X0] : add(additive_inverse(X0),additive_identity) = multiply(X0,additive_inverse(multiply(X0,X0))),
    inference(superposition,[],[f49,f3813]) ).

fof(f3813,plain,
    ! [X0] : additive_identity = add(X0,multiply(X0,additive_inverse(multiply(X0,X0)))),
    inference(forward_demodulation,[],[f3772,f3650]) ).

fof(f3772,plain,
    ! [X0] : multiply(X0,additive_identity) = add(X0,multiply(X0,additive_inverse(multiply(X0,X0)))),
    inference(superposition,[],[f176,f3]) ).

fof(f176,plain,
    ! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,multiply(X0,X0))),
    inference(forward_demodulation,[],[f160,f6]) ).

fof(f160,plain,
    ! [X0,X1] : multiply(X0,add(X1,multiply(X0,X0))) = add(multiply(X0,X1),X0),
    inference(superposition,[],[f8,f10]) ).

fof(f12889,plain,
    ! [X0] : additive_identity = add(multiply(X0,X0),multiply(X0,multiply(X0,additive_inverse(multiply(X0,X0))))),
    inference(forward_demodulation,[],[f12847,f7]) ).

fof(f12847,plain,
    ! [X0] : additive_identity = add(multiply(X0,X0),multiply(multiply(X0,X0),additive_inverse(multiply(X0,X0)))),
    inference(superposition,[],[f3813,f5741]) ).

fof(f5741,plain,
    ! [X0] : multiply(X0,X0) = multiply(multiply(X0,X0),multiply(X0,X0)),
    inference(superposition,[],[f75,f10]) ).

fof(f75,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(multiply(X0,X1),multiply(X0,multiply(X1,multiply(X0,X1)))),
    inference(superposition,[],[f10,f7]) ).

fof(f157,plain,
    ! [X0,X1] : multiply(a,add(multiply(b,X0),X1)) = add(multiply(c,X0),multiply(a,X1)),
    inference(superposition,[],[f8,f71]) ).

fof(f138,plain,
    ! [X0,X1] : additive_inverse(X0) = add(additive_inverse(add(X0,X1)),X1),
    inference(superposition,[],[f91,f49]) ).

fof(f91,plain,
    ! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
    inference(superposition,[],[f49,f6]) ).

fof(f24292,plain,
    ! [X0] : multiply(additive_identity,X0) = multiply(add(a,additive_inverse(multiply(c,b))),multiply(b,X0)),
    inference(superposition,[],[f419,f14668]) ).

fof(f14668,plain,
    additive_identity = add(c,multiply(additive_inverse(multiply(c,b)),b)),
    inference(forward_demodulation,[],[f14667,f426]) ).

fof(f426,plain,
    additive_identity = multiply(additive_identity,b),
    inference(forward_demodulation,[],[f424,f3]) ).

fof(f424,plain,
    add(additive_inverse(c),c) = multiply(additive_identity,b),
    inference(superposition,[],[f49,f420]) ).

fof(f420,plain,
    c = add(c,multiply(additive_identity,b)),
    inference(forward_demodulation,[],[f411,f11]) ).

fof(f411,plain,
    multiply(a,b) = add(c,multiply(additive_identity,b)),
    inference(superposition,[],[f244,f2]) ).

fof(f244,plain,
    ! [X0] : multiply(add(a,X0),b) = add(c,multiply(X0,b)),
    inference(superposition,[],[f9,f11]) ).

fof(f14667,plain,
    multiply(additive_identity,b) = add(c,multiply(additive_inverse(multiply(c,b)),b)),
    inference(forward_demodulation,[],[f14617,f686]) ).

fof(f14617,plain,
    ! [X0] : multiply(additive_identity,b) = add(c,multiply(add(X0,additive_inverse(add(multiply(c,b),X0))),b)),
    inference(superposition,[],[f7859,f39]) ).

fof(f7859,plain,
    ! [X0] : add(c,multiply(X0,b)) = multiply(add(multiply(c,b),X0),b),
    inference(superposition,[],[f237,f84]) ).

fof(f84,plain,
    c = multiply(c,multiply(b,b)),
    inference(forward_demodulation,[],[f82,f11]) ).

fof(f82,plain,
    multiply(a,b) = multiply(c,multiply(b,b)),
    inference(superposition,[],[f71,f10]) ).

fof(f237,plain,
    ! [X2,X3,X0,X1] : multiply(add(multiply(X0,X1),X3),X2) = add(multiply(X0,multiply(X1,X2)),multiply(X3,X2)),
    inference(superposition,[],[f9,f7]) ).

fof(f419,plain,
    ! [X0,X1] : multiply(add(a,X0),multiply(b,X1)) = multiply(add(c,multiply(X0,b)),X1),
    inference(superposition,[],[f7,f244]) ).

fof(f27401,plain,
    multiply(b,add(a,multiply(c,additive_inverse(b)))) = multiply(b,multiply(add(a,multiply(c,additive_inverse(b))),multiply(b,additive_identity))),
    inference(superposition,[],[f80,f24409]) ).

fof(f80,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1))))),
    inference(forward_demodulation,[],[f74,f7]) ).

fof(f74,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X1,multiply(multiply(X0,X1),multiply(X0,X1)))),
    inference(superposition,[],[f7,f10]) ).

fof(f153553,plain,
    multiply(a,c) = multiply(a,multiply(b,multiply(c,b))),
    inference(forward_demodulation,[],[f153504,f148389]) ).

fof(f148389,plain,
    multiply(c,b) = multiply(c,multiply(a,c)),
    inference(forward_demodulation,[],[f148388,f122331]) ).

fof(f148388,plain,
    multiply(c,multiply(a,c)) = additive_inverse(multiply(c,additive_inverse(b))),
    inference(forward_demodulation,[],[f148331,f122331]) ).

fof(f148331,plain,
    additive_inverse(multiply(c,additive_inverse(b))) = multiply(c,additive_inverse(multiply(a,additive_inverse(c)))),
    inference(superposition,[],[f121719,f121913]) ).

fof(f121913,plain,
    multiply(c,additive_inverse(b)) = multiply(c,multiply(a,additive_inverse(c))),
    inference(forward_demodulation,[],[f121912,f22043]) ).

fof(f121912,plain,
    additive_inverse(multiply(c,b)) = multiply(c,multiply(a,additive_inverse(c))),
    inference(forward_demodulation,[],[f121179,f2]) ).

fof(f121179,plain,
    add(additive_inverse(multiply(c,b)),additive_identity) = multiply(c,multiply(a,additive_inverse(c))),
    inference(superposition,[],[f169,f49003]) ).

fof(f49003,plain,
    additive_identity = multiply(c,add(b,multiply(a,additive_inverse(c)))),
    inference(forward_demodulation,[],[f49002,f3650]) ).

fof(f49002,plain,
    multiply(c,additive_identity) = multiply(c,add(b,multiply(a,additive_inverse(c)))),
    inference(forward_demodulation,[],[f48967,f29138]) ).

fof(f29138,plain,
    ! [X0] : additive_identity = multiply(add(b,multiply(a,additive_inverse(c))),multiply(c,X0)),
    inference(superposition,[],[f24230,f71]) ).

fof(f24230,plain,
    ! [X0] : additive_identity = multiply(add(b,multiply(a,additive_inverse(c))),multiply(a,X0)),
    inference(forward_demodulation,[],[f24207,f5232]) ).

fof(f24207,plain,
    ! [X0] : multiply(additive_identity,X0) = multiply(add(b,multiply(a,additive_inverse(c))),multiply(a,X0)),
    inference(superposition,[],[f7,f24084]) ).

fof(f24084,plain,
    additive_identity = multiply(add(b,multiply(a,additive_inverse(c))),a),
    inference(forward_demodulation,[],[f24083,f3650]) ).

fof(f24083,plain,
    multiply(add(b,multiply(a,additive_inverse(c))),additive_identity) = multiply(add(b,multiply(a,additive_inverse(c))),a),
    inference(forward_demodulation,[],[f24034,f22871]) ).

fof(f22871,plain,
    ! [X0] : additive_identity = multiply(a,multiply(add(b,multiply(a,additive_inverse(c))),X0)),
    inference(forward_demodulation,[],[f22870,f5232]) ).

fof(f22870,plain,
    ! [X0] : multiply(additive_identity,X0) = multiply(a,multiply(add(b,multiply(a,additive_inverse(c))),X0)),
    inference(forward_demodulation,[],[f22869,f516]) ).

fof(f516,plain,
    additive_inverse(c) = multiply(additive_inverse(a),b),
    inference(forward_demodulation,[],[f514,f2]) ).

fof(f514,plain,
    add(additive_inverse(c),additive_identity) = multiply(additive_inverse(a),b),
    inference(superposition,[],[f49,f512]) ).

fof(f512,plain,
    additive_identity = add(c,multiply(additive_inverse(a),b)),
    inference(forward_demodulation,[],[f414,f426]) ).

fof(f414,plain,
    multiply(additive_identity,b) = add(c,multiply(additive_inverse(a),b)),
    inference(superposition,[],[f244,f4]) ).

fof(f22869,plain,
    ! [X0] : multiply(additive_identity,X0) = multiply(a,multiply(add(b,multiply(a,multiply(additive_inverse(a),b))),X0)),
    inference(forward_demodulation,[],[f22868,f7]) ).

fof(f22868,plain,
    ! [X0] : multiply(additive_identity,X0) = multiply(a,multiply(add(b,multiply(multiply(a,additive_inverse(a)),b)),X0)),
    inference(forward_demodulation,[],[f22721,f15817]) ).

fof(f15817,plain,
    ! [X0] : additive_inverse(multiply(X0,X0)) = multiply(X0,additive_inverse(X0)),
    inference(forward_demodulation,[],[f15816,f1]) ).

fof(f15816,plain,
    ! [X0] : additive_inverse(multiply(X0,X0)) = add(additive_identity,multiply(X0,additive_inverse(X0))),
    inference(forward_demodulation,[],[f15761,f13]) ).

fof(f15761,plain,
    ! [X0] : additive_inverse(multiply(X0,X0)) = add(additive_inverse(additive_identity),multiply(X0,additive_inverse(X0))),
    inference(superposition,[],[f138,f12890]) ).

fof(f22721,plain,
    ! [X0] : multiply(additive_identity,X0) = multiply(a,multiply(add(b,multiply(additive_inverse(multiply(a,a)),b)),X0)),
    inference(superposition,[],[f190,f11374]) ).

fof(f11374,plain,
    additive_identity = add(c,multiply(a,multiply(additive_inverse(multiply(a,a)),b))),
    inference(forward_demodulation,[],[f11373,f426]) ).

fof(f11373,plain,
    multiply(additive_identity,b) = add(c,multiply(a,multiply(additive_inverse(multiply(a,a)),b))),
    inference(forward_demodulation,[],[f11307,f7]) ).

fof(f11307,plain,
    multiply(additive_identity,b) = add(c,multiply(multiply(a,additive_inverse(multiply(a,a))),b)),
    inference(superposition,[],[f244,f3813]) ).

fof(f190,plain,
    ! [X0,X1] : multiply(a,multiply(add(b,X0),X1)) = multiply(add(c,multiply(a,X0)),X1),
    inference(superposition,[],[f7,f156]) ).

fof(f24034,plain,
    multiply(add(b,multiply(a,additive_inverse(c))),a) = multiply(add(b,multiply(a,additive_inverse(c))),multiply(a,multiply(add(b,multiply(a,additive_inverse(c))),additive_identity))),
    inference(superposition,[],[f80,f22871]) ).

fof(f48967,plain,
    multiply(c,multiply(add(b,multiply(a,additive_inverse(c))),multiply(c,additive_identity))) = multiply(c,add(b,multiply(a,additive_inverse(c)))),
    inference(superposition,[],[f80,f29138]) ).

fof(f153504,plain,
    multiply(a,c) = multiply(a,multiply(b,multiply(c,multiply(a,c)))),
    inference(superposition,[],[f6316,f153159]) ).

fof(f153159,plain,
    multiply(a,c) = multiply(c,multiply(b,c)),
    inference(superposition,[],[f150475,f2]) ).

fof(f150475,plain,
    multiply(a,c) = add(multiply(c,multiply(b,c)),additive_identity),
    inference(forward_demodulation,[],[f150474,f63]) ).

fof(f150474,plain,
    multiply(a,c) = add(multiply(c,multiply(b,additive_inverse(additive_inverse(c)))),additive_identity),
    inference(forward_demodulation,[],[f150473,f123921]) ).

fof(f123921,plain,
    ! [X2,X0] : multiply(additive_inverse(X0),X2) = multiply(X0,additive_inverse(X2)),
    inference(forward_demodulation,[],[f123920,f686]) ).

fof(f123920,plain,
    ! [X2,X0,X1] : multiply(X0,additive_inverse(X2)) = multiply(add(X1,additive_inverse(add(X0,X1))),X2),
    inference(forward_demodulation,[],[f123919,f2]) ).

fof(f123919,plain,
    ! [X2,X0,X1] : multiply(add(X1,additive_inverse(add(X0,X1))),X2) = add(multiply(X0,additive_inverse(X2)),additive_identity),
    inference(forward_demodulation,[],[f123474,f5232]) ).

fof(f123474,plain,
    ! [X2,X0,X1] : multiply(add(X1,additive_inverse(add(X0,X1))),X2) = add(multiply(X0,additive_inverse(X2)),multiply(additive_identity,X2)),
    inference(superposition,[],[f123156,f39]) ).

fof(f123156,plain,
    ! [X2,X0,X1] : multiply(X2,X1) = add(multiply(X0,additive_inverse(X1)),multiply(add(X0,X2),X1)),
    inference(forward_demodulation,[],[f263,f121719]) ).

fof(f263,plain,
    ! [X2,X0,X1] : multiply(X2,X1) = add(additive_inverse(multiply(X0,X1)),multiply(add(X0,X2),X1)),
    inference(superposition,[],[f49,f9]) ).

fof(f150473,plain,
    multiply(a,c) = add(multiply(c,multiply(additive_inverse(b),additive_inverse(c))),additive_identity),
    inference(forward_demodulation,[],[f149681,f7]) ).

fof(f149681,plain,
    multiply(a,c) = add(multiply(multiply(c,additive_inverse(b)),additive_inverse(c)),additive_identity),
    inference(superposition,[],[f148771,f119222]) ).

fof(f119222,plain,
    additive_identity = multiply(add(a,multiply(c,additive_inverse(b))),c),
    inference(forward_demodulation,[],[f119221,f3650]) ).

fof(f119221,plain,
    multiply(c,additive_identity) = multiply(add(a,multiply(c,additive_inverse(b))),c),
    inference(forward_demodulation,[],[f119220,f3650]) ).

fof(f119220,plain,
    multiply(c,multiply(additive_inverse(b),additive_identity)) = multiply(add(a,multiply(c,additive_inverse(b))),c),
    inference(forward_demodulation,[],[f119219,f7]) ).

fof(f119219,plain,
    multiply(multiply(c,additive_inverse(b)),additive_identity) = multiply(add(a,multiply(c,additive_inverse(b))),c),
    inference(forward_demodulation,[],[f119218,f267]) ).

fof(f267,plain,
    ! [X0] : multiply(add(a,X0),additive_identity) = multiply(X0,additive_identity),
    inference(forward_demodulation,[],[f238,f1]) ).

fof(f238,plain,
    ! [X0] : multiply(add(a,X0),additive_identity) = add(additive_identity,multiply(X0,additive_identity)),
    inference(superposition,[],[f9,f197]) ).

fof(f119218,plain,
    multiply(add(a,multiply(c,additive_inverse(b))),additive_identity) = multiply(add(a,multiply(c,additive_inverse(b))),c),
    inference(forward_demodulation,[],[f119148,f27856]) ).

fof(f27856,plain,
    ! [X0] : additive_identity = multiply(c,multiply(add(a,multiply(c,additive_inverse(b))),X0)),
    inference(forward_demodulation,[],[f27828,f5232]) ).

fof(f27828,plain,
    ! [X0] : multiply(additive_identity,X0) = multiply(c,multiply(add(a,multiply(c,additive_inverse(b))),X0)),
    inference(superposition,[],[f7,f27773]) ).

fof(f27773,plain,
    additive_identity = multiply(c,add(a,multiply(c,additive_inverse(b)))),
    inference(forward_demodulation,[],[f27772,f197]) ).

fof(f27772,plain,
    multiply(a,additive_identity) = multiply(c,add(a,multiply(c,additive_inverse(b)))),
    inference(forward_demodulation,[],[f27737,f6]) ).

fof(f27737,plain,
    multiply(a,additive_identity) = multiply(c,add(multiply(c,additive_inverse(b)),a)),
    inference(superposition,[],[f19407,f27436]) ).

fof(f19407,plain,
    ! [X0,X1] : multiply(c,add(X0,X1)) = multiply(a,multiply(b,add(X1,X0))),
    inference(superposition,[],[f71,f4102]) ).

fof(f4102,plain,
    ! [X2,X0,X1] : multiply(X0,add(X1,X2)) = multiply(X0,add(X2,X1)),
    inference(superposition,[],[f166,f8]) ).

fof(f166,plain,
    ! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X2),multiply(X0,X1)),
    inference(superposition,[],[f8,f6]) ).

fof(f119148,plain,
    multiply(add(a,multiply(c,additive_inverse(b))),multiply(c,multiply(add(a,multiply(c,additive_inverse(b))),additive_identity))) = multiply(add(a,multiply(c,additive_inverse(b))),c),
    inference(superposition,[],[f80,f27856]) ).

fof(f148771,plain,
    ! [X2,X0,X1] : multiply(X2,X1) = add(multiply(X0,additive_inverse(X1)),multiply(add(X2,X0),X1)),
    inference(forward_demodulation,[],[f4967,f121719]) ).

fof(f4967,plain,
    ! [X2,X0,X1] : multiply(X2,X1) = add(additive_inverse(multiply(X0,X1)),multiply(add(X2,X0),X1)),
    inference(superposition,[],[f49,f259]) ).

fof(f6316,plain,
    ! [X0] : multiply(c,X0) = multiply(a,multiply(b,multiply(c,multiply(c,X0)))),
    inference(forward_demodulation,[],[f6315,f7]) ).

fof(f6315,plain,
    ! [X0] : multiply(c,X0) = multiply(a,multiply(b,multiply(multiply(c,c),X0))),
    inference(forward_demodulation,[],[f6303,f7]) ).

fof(f6303,plain,
    ! [X0] : multiply(c,X0) = multiply(a,multiply(multiply(b,multiply(c,c)),X0)),
    inference(superposition,[],[f7,f6201]) ).

fof(f6201,plain,
    c = multiply(a,multiply(b,multiply(c,c))),
    inference(forward_demodulation,[],[f6003,f71]) ).

fof(f6003,plain,
    c = multiply(a,multiply(b,multiply(a,multiply(b,c)))),
    inference(superposition,[],[f80,f11]) ).

fof(f143191,plain,
    multiply(b,a) = multiply(a,multiply(c,a)),
    inference(forward_demodulation,[],[f143190,f122331]) ).

fof(f143190,plain,
    multiply(b,a) = multiply(a,additive_inverse(multiply(c,additive_inverse(a)))),
    inference(forward_demodulation,[],[f143149,f122331]) ).

fof(f143149,plain,
    multiply(a,additive_inverse(multiply(c,additive_inverse(a)))) = additive_inverse(multiply(b,additive_inverse(a))),
    inference(superposition,[],[f121719,f139825]) ).

fof(f139825,plain,
    multiply(b,additive_inverse(a)) = multiply(a,multiply(c,additive_inverse(a))),
    inference(forward_demodulation,[],[f139788,f123921]) ).

fof(f139788,plain,
    multiply(b,additive_inverse(a)) = multiply(a,multiply(additive_inverse(c),a)),
    inference(superposition,[],[f124246,f7]) ).

fof(f124246,plain,
    multiply(b,additive_inverse(a)) = multiply(multiply(a,additive_inverse(c)),a),
    inference(forward_demodulation,[],[f123738,f2]) ).

fof(f123738,plain,
    multiply(multiply(a,additive_inverse(c)),a) = add(multiply(b,additive_inverse(a)),additive_identity),
    inference(superposition,[],[f123156,f24084]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : RNG009-7 : TPTP v8.2.0. Released v1.0.0.
% 0.06/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33  % Computer : n005.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Sat May 18 12:24:38 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.11/0.33  % (5944)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35  % (5947)WARNING: value z3 for option sas not known
% 0.11/0.35  % (5945)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.35  % (5946)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.35  % (5947)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.35  % (5950)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.35  % (5949)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.35  % (5951)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.35  % (5948)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.35  TRYING [1]
% 0.11/0.35  TRYING [2]
% 0.11/0.35  TRYING [3]
% 0.11/0.35  TRYING [1]
% 0.11/0.35  TRYING [2]
% 0.11/0.36  TRYING [3]
% 0.11/0.36  TRYING [4]
% 0.11/0.38  TRYING [4]
% 0.17/0.40  TRYING [5]
% 0.17/0.49  TRYING [5]
% 0.17/0.51  TRYING [6]
% 3.61/0.92  TRYING [7]
% 4.26/0.98  TRYING [6]
% 7.73/1.45  TRYING [1]
% 7.73/1.45  TRYING [2]
% 7.73/1.45  TRYING [3]
% 7.97/1.46  TRYING [4]
% 7.97/1.51  TRYING [5]
% 8.74/1.63  TRYING [6]
% 12.12/2.11  TRYING [8]
% 12.55/2.15  TRYING [7]
% 24.37/3.83  TRYING [8]
% 33.86/5.21  TRYING [7]
% 49.76/7.51  TRYING [9]
% 51.26/7.70  % (5947)First to succeed.
% 51.26/7.70  % (5947)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5944"
% 51.26/7.71  % (5947)Refutation found. Thanks to Tanya!
% 51.26/7.71  % SZS status Unsatisfiable for theBenchmark
% 51.26/7.71  % SZS output start Proof for theBenchmark
% See solution above
% 51.61/7.71  % (5947)------------------------------
% 51.61/7.71  % (5947)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 51.61/7.71  % (5947)Termination reason: Refutation
% 51.61/7.71  
% 51.61/7.71  % (5947)Memory used [KB]: 66904
% 51.61/7.71  % (5947)Time elapsed: 7.355 s
% 51.61/7.71  % (5947)Instructions burned: 19455 (million)
% 51.61/7.71  % (5944)Success in time 7.367 s
%------------------------------------------------------------------------------