TSTP Solution File: GRP100-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP100-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n032.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 Apr 30 11:51:32 EDT 2024

% Result   : Unsatisfiable 3.48s 0.82s
% Output   : Refutation 3.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   39
%            Number of leaves      :    9
% Syntax   : Number of formulae    :  112 (  31 unt;   0 def)
%            Number of atoms       :  207 ( 106 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  184 (  89   ~;  91   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   5 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :  151 ( 151   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f27609,plain,
    $false,
    inference(avatar_sat_refutation,[],[f227,f388,f529,f6078,f6080,f27466]) ).

fof(f27466,plain,
    ( spl0_1
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f27465]) ).

fof(f27465,plain,
    ( $false
    | spl0_1
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f27464]) ).

fof(f27464,plain,
    ( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
    | spl0_1
    | ~ spl0_4 ),
    inference(superposition,[],[f214,f21139]) ).

fof(f21139,plain,
    ( ! [X2,X0,X1] : multiply(X0,multiply(X2,X1)) = multiply(multiply(X0,X2),X1)
    | ~ spl0_4 ),
    inference(superposition,[],[f2310,f19568]) ).

fof(f19568,plain,
    ( ! [X2,X0,X1] : multiply(X2,X0) = double_divide(X1,double_divide(X0,multiply(X1,X2)))
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f19567,f9]) ).

fof(f9,plain,
    ! [X0,X1] : multiply(X1,X0) = inverse(double_divide(X0,X1)),
    inference(superposition,[],[f2,f3]) ).

fof(f3,axiom,
    ! [X0] : inverse(X0) = double_divide(X0,identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).

fof(f2,axiom,
    ! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).

fof(f19567,plain,
    ( ! [X2,X0,X1] : multiply(X2,X0) = double_divide(X1,double_divide(X0,inverse(double_divide(X2,X1))))
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f19566,f2344]) ).

fof(f2344,plain,
    ( ! [X0,X1] : double_divide(X0,inverse(X1)) = multiply(X1,inverse(X0))
    | ~ spl0_4 ),
    inference(superposition,[],[f1484,f2302]) ).

fof(f2302,plain,
    ( ! [X0,X1] : multiply(X1,double_divide(X1,inverse(X0))) = X0
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f1507,f505]) ).

fof(f505,plain,
    ( ! [X0,X1] : double_divide(X0,X1) = inverse(multiply(X1,X0))
    | ~ spl0_4 ),
    inference(superposition,[],[f490,f12]) ).

fof(f12,plain,
    ! [X0,X1] : multiply(identity,double_divide(X0,X1)) = inverse(multiply(X1,X0)),
    inference(forward_demodulation,[],[f8,f3]) ).

fof(f8,plain,
    ! [X0,X1] : multiply(identity,double_divide(X0,X1)) = double_divide(multiply(X1,X0),identity),
    inference(superposition,[],[f2,f2]) ).

fof(f490,plain,
    ( ! [X0] : multiply(identity,X0) = X0
    | ~ spl0_4 ),
    inference(superposition,[],[f476,f6]) ).

fof(f6,plain,
    ! [X0] : multiply(identity,X0) = double_divide(inverse(X0),identity),
    inference(superposition,[],[f2,f3]) ).

fof(f476,plain,
    ( ! [X0] : double_divide(inverse(X0),identity) = X0
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f475,f3]) ).

fof(f475,plain,
    ( ! [X0] : double_divide(double_divide(X0,identity),identity) = X0
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f461,f225]) ).

fof(f225,plain,
    ( identity = inverse(identity)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f224]) ).

fof(f224,plain,
    ( spl0_4
  <=> identity = inverse(identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f461,plain,
    ( ! [X0] : double_divide(double_divide(X0,inverse(identity)),identity) = X0
    | ~ spl0_4 ),
    inference(superposition,[],[f430,f11]) ).

fof(f11,plain,
    ! [X0] : multiply(inverse(X0),X0) = inverse(identity),
    inference(forward_demodulation,[],[f7,f3]) ).

fof(f7,plain,
    ! [X0] : double_divide(identity,identity) = multiply(inverse(X0),X0),
    inference(superposition,[],[f2,f4]) ).

fof(f4,axiom,
    ! [X0] : identity = double_divide(X0,inverse(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).

fof(f430,plain,
    ( ! [X0,X1] : double_divide(double_divide(X0,multiply(inverse(X0),X1)),identity) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f429,f3]) ).

fof(f429,plain,
    ( ! [X0,X1] : double_divide(double_divide(X0,multiply(double_divide(X0,identity),X1)),identity) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f428,f9]) ).

fof(f428,plain,
    ( ! [X0,X1] : double_divide(double_divide(X0,inverse(double_divide(X1,double_divide(X0,identity)))),identity) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f411,f3]) ).

fof(f411,plain,
    ( ! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,identity)),identity)),identity) = X1
    | ~ spl0_4 ),
    inference(superposition,[],[f52,f225]) ).

fof(f52,plain,
    ! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2))),inverse(identity)) = X1,
    inference(forward_demodulation,[],[f51,f3]) ).

fof(f51,plain,
    ! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),inverse(identity)) = X1,
    inference(forward_demodulation,[],[f1,f3]) ).

fof(f1,axiom,
    ! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),double_divide(identity,identity)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).

fof(f1507,plain,
    ( ! [X0,X1] : multiply(X1,inverse(multiply(inverse(X0),X1))) = X0
    | ~ spl0_4 ),
    inference(superposition,[],[f1484,f465]) ).

fof(f465,plain,
    ( ! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1
    | ~ spl0_4 ),
    inference(superposition,[],[f430,f2]) ).

fof(f1484,plain,
    ( ! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f1483,f490]) ).

fof(f1483,plain,
    ( ! [X0,X1] : multiply(multiply(multiply(identity,X0),X1),inverse(X0)) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f1482,f490]) ).

fof(f1482,plain,
    ( ! [X0,X1] : multiply(multiply(multiply(identity,multiply(identity,X0)),X1),inverse(X0)) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f1460,f490]) ).

fof(f1460,plain,
    ( ! [X0,X1] : multiply(multiply(multiply(identity,multiply(identity,X0)),X1),multiply(identity,inverse(X0))) = X1
    | ~ spl0_4 ),
    inference(superposition,[],[f465,f62]) ).

fof(f62,plain,
    ! [X0] : multiply(identity,multiply(identity,X0)) = inverse(multiply(identity,inverse(X0))),
    inference(superposition,[],[f12,f6]) ).

fof(f19566,plain,
    ( ! [X2,X0,X1] : multiply(X2,X0) = double_divide(X1,multiply(double_divide(X2,X1),inverse(X0)))
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f19565,f9]) ).

fof(f19565,plain,
    ( ! [X2,X0,X1] : double_divide(X1,multiply(double_divide(X2,X1),inverse(X0))) = inverse(double_divide(X0,X2))
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f19322,f3]) ).

fof(f19322,plain,
    ( ! [X2,X0,X1] : double_divide(X1,multiply(double_divide(X2,X1),inverse(X0))) = double_divide(double_divide(X0,X2),identity)
    | ~ spl0_4 ),
    inference(superposition,[],[f430,f8671]) ).

fof(f8671,plain,
    ( ! [X2,X0,X1] : multiply(X1,double_divide(X0,multiply(double_divide(X2,X0),X1))) = X2
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f8670,f9]) ).

fof(f8670,plain,
    ( ! [X2,X0,X1] : multiply(X1,double_divide(X0,inverse(double_divide(X1,double_divide(X2,X0))))) = X2
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f8669,f2344]) ).

fof(f8669,plain,
    ( ! [X2,X0,X1] : multiply(X1,multiply(double_divide(X1,double_divide(X2,X0)),inverse(X0))) = X2
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f8474,f9]) ).

fof(f8474,plain,
    ( ! [X2,X0,X1] : multiply(X1,inverse(double_divide(inverse(X0),double_divide(X1,double_divide(X2,X0))))) = X2
    | ~ spl0_4 ),
    inference(superposition,[],[f1484,f7293]) ).

fof(f7293,plain,
    ( ! [X2,X0,X1] : multiply(double_divide(inverse(X2),double_divide(X1,double_divide(X0,X2))),X0) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f623,f4718]) ).

fof(f4718,plain,
    ( ! [X0,X1] : double_divide(X1,X0) = double_divide(X0,X1)
    | ~ spl0_4 ),
    inference(superposition,[],[f4586,f2599]) ).

fof(f2599,plain,
    ( ! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f2520,f242]) ).

fof(f242,plain,
    ! [X0] : double_divide(inverse(X0),inverse(identity)) = X0,
    inference(forward_demodulation,[],[f235,f3]) ).

fof(f235,plain,
    ! [X0] : double_divide(double_divide(X0,identity),inverse(identity)) = X0,
    inference(superposition,[],[f137,f19]) ).

fof(f19,plain,
    ! [X0] : identity = double_divide(inverse(X0),multiply(identity,X0)),
    inference(superposition,[],[f4,f13]) ).

fof(f13,plain,
    ! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
    inference(superposition,[],[f6,f3]) ).

fof(f137,plain,
    ! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),multiply(identity,X0))),inverse(identity)) = X1,
    inference(forward_demodulation,[],[f136,f3]) ).

fof(f136,plain,
    ! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,identity),multiply(identity,X0))),inverse(identity)) = X1,
    inference(forward_demodulation,[],[f120,f13]) ).

fof(f120,plain,
    ! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,identity),inverse(inverse(X0)))),inverse(identity)) = X1,
    inference(superposition,[],[f52,f4]) ).

fof(f2520,plain,
    ( ! [X0,X1] : double_divide(inverse(X1),inverse(identity)) = double_divide(double_divide(X0,X1),X0)
    | ~ spl0_4 ),
    inference(superposition,[],[f246,f2311]) ).

fof(f2311,plain,
    ( ! [X0,X1] : inverse(X0) = multiply(X1,double_divide(X1,X0))
    | ~ spl0_4 ),
    inference(superposition,[],[f2302,f491]) ).

fof(f491,plain,
    ( ! [X0] : inverse(inverse(X0)) = X0
    | ~ spl0_4 ),
    inference(superposition,[],[f476,f3]) ).

fof(f246,plain,
    ! [X0,X1] : double_divide(X0,X1) = double_divide(multiply(X1,X0),inverse(identity)),
    inference(superposition,[],[f242,f9]) ).

fof(f4586,plain,
    ( ! [X0,X1] : double_divide(double_divide(X1,X0),X0) = X1
    | ~ spl0_4 ),
    inference(superposition,[],[f2457,f485]) ).

fof(f485,plain,
    ( ! [X0,X1] : double_divide(X0,X1) = double_divide(multiply(X1,X0),identity)
    | ~ spl0_4 ),
    inference(superposition,[],[f476,f9]) ).

fof(f2457,plain,
    ( ! [X0,X1] : double_divide(multiply(X0,double_divide(X1,X0)),identity) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f2456,f490]) ).

fof(f2456,plain,
    ( ! [X0,X1] : double_divide(multiply(multiply(identity,X0),double_divide(X1,X0)),identity) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f2455,f13]) ).

fof(f2455,plain,
    ( ! [X0,X1] : double_divide(multiply(inverse(inverse(X0)),double_divide(X1,X0)),identity) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f2454,f9]) ).

fof(f2454,plain,
    ( ! [X0,X1] : double_divide(inverse(double_divide(double_divide(X1,X0),inverse(inverse(X0)))),identity) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f2453,f977]) ).

fof(f977,plain,
    ( ! [X0] : inverse(X0) = double_divide(identity,X0)
    | ~ spl0_4 ),
    inference(superposition,[],[f491,f896]) ).

fof(f896,plain,
    ( ! [X0] : inverse(double_divide(identity,X0)) = X0
    | ~ spl0_4 ),
    inference(superposition,[],[f673,f3]) ).

fof(f673,plain,
    ( ! [X0] : double_divide(double_divide(identity,X0),identity) = X0
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f672,f490]) ).

fof(f672,plain,
    ( ! [X0] : double_divide(double_divide(identity,multiply(identity,X0)),identity) = X0
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f671,f9]) ).

fof(f671,plain,
    ( ! [X0] : double_divide(double_divide(identity,inverse(double_divide(X0,identity))),identity) = X0
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f670,f3]) ).

fof(f670,plain,
    ( ! [X0] : double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),identity) = X0
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f605,f225]) ).

fof(f605,plain,
    ( ! [X0] : double_divide(double_divide(identity,double_divide(double_divide(X0,identity),inverse(identity))),identity) = X0
    | ~ spl0_4 ),
    inference(superposition,[],[f392,f402]) ).

fof(f402,plain,
    ( identity = double_divide(identity,identity)
    | ~ spl0_4 ),
    inference(superposition,[],[f4,f225]) ).

fof(f392,plain,
    ( ! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2))),identity) = X1
    | ~ spl0_4 ),
    inference(superposition,[],[f52,f225]) ).

fof(f2453,plain,
    ( ! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(X1,X0),inverse(inverse(X0)))),identity) = X1
    | ~ spl0_4 ),
    inference(forward_demodulation,[],[f2431,f225]) ).

fof(f2431,plain,
    ( ! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(X1,X0),inverse(inverse(X0)))),inverse(identity)) = X1
    | ~ spl0_4 ),
    inference(superposition,[],[f52,f2324]) ).

fof(f2324,plain,
    ( ! [X0] : double_divide(identity,inverse(X0)) = X0
    | ~ spl0_4 ),
    inference(superposition,[],[f2302,f490]) ).

fof(f623,plain,
    ( ! [X2,X0,X1] : multiply(double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2)),X0) = X1
    | ~ spl0_4 ),
    inference(superposition,[],[f392,f2]) ).

fof(f2310,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = multiply(X2,double_divide(X2,double_divide(X1,X0)))
    | ~ spl0_4 ),
    inference(superposition,[],[f2302,f505]) ).

fof(f214,plain,
    ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | spl0_1 ),
    inference(avatar_component_clause,[],[f212]) ).

fof(f212,plain,
    ( spl0_1
  <=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f6080,plain,
    ( spl0_2
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f6079]) ).

fof(f6079,plain,
    ( $false
    | spl0_2
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f6026]) ).

fof(f6026,plain,
    ( multiply(a4,b4) != multiply(a4,b4)
    | spl0_2
    | ~ spl0_4 ),
    inference(superposition,[],[f218,f5815]) ).

fof(f5815,plain,
    ( ! [X0,X1] : multiply(X0,X1) = multiply(X1,X0)
    | ~ spl0_4 ),
    inference(superposition,[],[f4776,f9]) ).

fof(f4776,plain,
    ( ! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1))
    | ~ spl0_4 ),
    inference(superposition,[],[f2664,f4586]) ).

fof(f2664,plain,
    ( ! [X0,X1] : inverse(X0) = multiply(double_divide(X0,X1),X1)
    | ~ spl0_4 ),
    inference(superposition,[],[f2311,f2599]) ).

fof(f218,plain,
    ( multiply(a4,b4) != multiply(b4,a4)
    | spl0_2 ),
    inference(avatar_component_clause,[],[f216]) ).

fof(f216,plain,
    ( spl0_2
  <=> multiply(a4,b4) = multiply(b4,a4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f6078,plain,
    ( spl0_2
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f6077]) ).

fof(f6077,plain,
    ( $false
    | spl0_2
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f6076]) ).

fof(f6076,plain,
    ( multiply(a4,b4) != multiply(a4,b4)
    | spl0_2
    | ~ spl0_4 ),
    inference(superposition,[],[f218,f5815]) ).

fof(f529,plain,
    ( spl0_3
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f528]) ).

fof(f528,plain,
    ( $false
    | spl0_3
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f527]) ).

fof(f527,plain,
    ( a2 != a2
    | spl0_3
    | ~ spl0_4 ),
    inference(superposition,[],[f222,f490]) ).

fof(f222,plain,
    ( a2 != multiply(identity,a2)
    | spl0_3 ),
    inference(avatar_component_clause,[],[f220]) ).

fof(f220,plain,
    ( spl0_3
  <=> a2 = multiply(identity,a2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f388,plain,
    spl0_4,
    inference(avatar_contradiction_clause,[],[f387]) ).

fof(f387,plain,
    ( $false
    | spl0_4 ),
    inference(subsumption_resolution,[],[f386,f226]) ).

fof(f226,plain,
    ( identity != inverse(identity)
    | spl0_4 ),
    inference(avatar_component_clause,[],[f224]) ).

fof(f386,plain,
    identity = inverse(identity),
    inference(forward_demodulation,[],[f376,f4]) ).

fof(f376,plain,
    inverse(identity) = double_divide(identity,inverse(identity)),
    inference(superposition,[],[f245,f359]) ).

fof(f359,plain,
    identity = multiply(identity,identity),
    inference(forward_demodulation,[],[f342,f242]) ).

fof(f342,plain,
    multiply(identity,identity) = double_divide(inverse(identity),inverse(identity)),
    inference(superposition,[],[f293,f3]) ).

fof(f293,plain,
    ! [X0] : multiply(identity,X0) = double_divide(double_divide(identity,X0),inverse(identity)),
    inference(forward_demodulation,[],[f285,f242]) ).

fof(f285,plain,
    ! [X0] : multiply(identity,X0) = double_divide(double_divide(identity,double_divide(inverse(X0),inverse(identity))),inverse(identity)),
    inference(superposition,[],[f119,f245]) ).

fof(f119,plain,
    ! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,inverse(X0)),inverse(identity))),inverse(identity)) = X1,
    inference(superposition,[],[f52,f3]) ).

fof(f245,plain,
    ! [X0] : inverse(X0) = double_divide(multiply(identity,X0),inverse(identity)),
    inference(superposition,[],[f242,f13]) ).

fof(f227,plain,
    ( ~ spl0_1
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f175,f224,f220,f216,f212]) ).

fof(f175,plain,
    ( identity != inverse(identity)
    | a2 != multiply(identity,a2)
    | multiply(a4,b4) != multiply(b4,a4)
    | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
    inference(forward_demodulation,[],[f5,f11]) ).

fof(f5,axiom,
    ( a2 != multiply(identity,a2)
    | identity != multiply(inverse(a1),a1)
    | multiply(a4,b4) != multiply(b4,a4)
    | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08  % Problem    : GRP100-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.04/0.09  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit   : 300
% 0.08/0.28  % WCLimit    : 300
% 0.08/0.28  % DateTime   : Tue Apr 30 04:41:36 EDT 2024
% 0.08/0.28  % CPUTime    : 
% 0.08/0.28  % (31352)Running in auto input_syntax mode. Trying TPTP
% 0.08/0.29  % (31355)WARNING: value z3 for option sas not known
% 0.08/0.29  % (31355)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)
% 0.08/0.29  % (31359)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)
% 0.08/0.30  % (31357)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)
% 0.08/0.30  % (31353)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.08/0.30  % (31354)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.08/0.30  % (31356)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.08/0.30  % (31358)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)
% 0.08/0.30  TRYING [1]
% 0.08/0.30  TRYING [1]
% 0.08/0.30  TRYING [2]
% 0.08/0.30  TRYING [2]
% 0.08/0.30  TRYING [3]
% 0.08/0.30  TRYING [3]
% 0.08/0.31  TRYING [4]
% 0.12/0.32  TRYING [5]
% 0.12/0.33  TRYING [4]
% 0.12/0.37  TRYING [6]
% 3.48/0.81  % (31355)First to succeed.
% 3.48/0.82  % (31355)Refutation found. Thanks to Tanya!
% 3.48/0.82  % SZS status Unsatisfiable for theBenchmark
% 3.48/0.82  % SZS output start Proof for theBenchmark
% See solution above
% 3.48/0.82  % (31355)------------------------------
% 3.48/0.82  % (31355)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 3.48/0.82  % (31355)Termination reason: Refutation
% 3.48/0.82  
% 3.48/0.82  % (31355)Memory used [KB]: 11670
% 3.48/0.82  % (31355)Time elapsed: 0.526 s
% 3.48/0.82  % (31355)Instructions burned: 2192 (million)
% 3.48/0.82  % (31355)------------------------------
% 3.48/0.82  % (31355)------------------------------
% 3.48/0.82  % (31352)Success in time 0.536 s
%------------------------------------------------------------------------------