TSTP Solution File: GRP659+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : GRP659+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n024.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 : Mon Jun 24 07:01:36 EDT 2024

% Result   : Theorem 10.11s 2.07s
% Output   : CNFRefutation 10.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   62 (  53 unt;   0 def)
%            Number of atoms       :   73 (  72 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   29 (  18   ~;   7   |;   3   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   0 con; 1-2 aty)
%            Number of variables   :  122 (   0 sgn  32   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).

fof(f2,axiom,
    ! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).

fof(f3,axiom,
    ! [X0,X1] : mult(rd(X1,X0),X0) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).

fof(f4,axiom,
    ! [X0,X1] : rd(mult(X1,X0),X0) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).

fof(f5,axiom,
    ! [X2,X0,X1] : mult(mult(X1,mult(X0,X2)),X0) = mult(mult(X1,X0),mult(X2,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).

fof(f6,conjecture,
    ? [X3] :
    ! [X4] :
      ( mult(X3,X4) = X4
      & mult(X4,X3) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f7,negated_conjecture,
    ~ ? [X3] :
      ! [X4] :
        ( mult(X3,X4) = X4
        & mult(X4,X3) = X4 ),
    inference(negated_conjecture,[],[f6]) ).

fof(f8,plain,
    ! [X0,X1,X2] : mult(mult(X2,mult(X1,X0)),X1) = mult(mult(X2,X1),mult(X0,X1)),
    inference(rectify,[],[f5]) ).

fof(f9,plain,
    ~ ? [X0] :
      ! [X1] :
        ( mult(X0,X1) = X1
        & mult(X1,X0) = X1 ),
    inference(rectify,[],[f7]) ).

fof(f10,plain,
    ! [X0] :
    ? [X1] :
      ( mult(X0,X1) != X1
      | mult(X1,X0) != X1 ),
    inference(ennf_transformation,[],[f9]) ).

fof(f11,plain,
    ! [X0] :
      ( ? [X1] :
          ( mult(X0,X1) != X1
          | mult(X1,X0) != X1 )
     => ( sK0(X0) != mult(X0,sK0(X0))
        | sK0(X0) != mult(sK0(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f12,plain,
    ! [X0] :
      ( sK0(X0) != mult(X0,sK0(X0))
      | sK0(X0) != mult(sK0(X0),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f11]) ).

fof(f13,plain,
    ! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
    inference(cnf_transformation,[],[f1]) ).

fof(f14,plain,
    ! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
    inference(cnf_transformation,[],[f2]) ).

fof(f15,plain,
    ! [X0,X1] : mult(rd(X1,X0),X0) = X1,
    inference(cnf_transformation,[],[f3]) ).

fof(f16,plain,
    ! [X0,X1] : rd(mult(X1,X0),X0) = X1,
    inference(cnf_transformation,[],[f4]) ).

fof(f17,plain,
    ! [X2,X0,X1] : mult(mult(X2,mult(X1,X0)),X1) = mult(mult(X2,X1),mult(X0,X1)),
    inference(cnf_transformation,[],[f8]) ).

fof(f18,plain,
    ! [X0] :
      ( sK0(X0) != mult(X0,sK0(X0))
      | sK0(X0) != mult(sK0(X0),X0) ),
    inference(cnf_transformation,[],[f12]) ).

cnf(c_49,plain,
    mult(X0,ld(X0,X1)) = X1,
    inference(cnf_transformation,[],[f13]) ).

cnf(c_50,plain,
    ld(X0,mult(X0,X1)) = X1,
    inference(cnf_transformation,[],[f14]) ).

cnf(c_51,plain,
    mult(rd(X0,X1),X1) = X0,
    inference(cnf_transformation,[],[f15]) ).

cnf(c_52,plain,
    rd(mult(X0,X1),X1) = X0,
    inference(cnf_transformation,[],[f16]) ).

cnf(c_53,plain,
    mult(mult(X0,mult(X1,X2)),X1) = mult(mult(X0,X1),mult(X2,X1)),
    inference(cnf_transformation,[],[f17]) ).

cnf(c_54,negated_conjecture,
    ( mult(sK0(X0),X0) != sK0(X0)
    | mult(X0,sK0(X0)) != sK0(X0) ),
    inference(cnf_transformation,[],[f18]) ).

cnf(c_82,negated_conjecture,
    ( mult(sK0(X0),X0) != sK0(X0)
    | mult(X0,sK0(X0)) != sK0(X0) ),
    inference(demodulation,[status(thm)],[c_54]) ).

cnf(c_130,plain,
    ld(rd(X0,X1),X0) = X1,
    inference(superposition,[status(thm)],[c_51,c_50]) ).

cnf(c_132,plain,
    rd(X0,ld(X1,X0)) = X1,
    inference(superposition,[status(thm)],[c_49,c_52]) ).

cnf(c_138,plain,
    mult(mult(rd(X0,mult(X1,X2)),X1),mult(X2,X1)) = mult(X0,X1),
    inference(superposition,[status(thm)],[c_51,c_53]) ).

cnf(c_140,plain,
    mult(mult(X0,X1),mult(ld(X1,X2),X1)) = mult(mult(X0,X2),X1),
    inference(superposition,[status(thm)],[c_49,c_53]) ).

cnf(c_163,plain,
    mult(rd(X0,mult(X1,X2)),X1) = rd(mult(X0,X1),mult(X2,X1)),
    inference(superposition,[status(thm)],[c_138,c_52]) ).

cnf(c_214,plain,
    mult(mult(rd(X0,X1),X2),X1) = mult(X0,mult(ld(X1,X2),X1)),
    inference(superposition,[status(thm)],[c_51,c_140]) ).

cnf(c_222,plain,
    ld(mult(X0,X1),mult(mult(X0,X2),X1)) = mult(ld(X1,X2),X1),
    inference(superposition,[status(thm)],[c_140,c_50]) ).

cnf(c_540,plain,
    mult(X0,mult(ld(X1,X1),X1)) = mult(X0,X1),
    inference(superposition,[status(thm)],[c_51,c_214]) ).

cnf(c_630,plain,
    ld(X0,mult(X0,X1)) = mult(ld(X1,X1),X1),
    inference(superposition,[status(thm)],[c_540,c_50]) ).

cnf(c_649,plain,
    mult(ld(X0,X0),X0) = X0,
    inference(light_normalisation,[status(thm)],[c_630,c_50]) ).

cnf(c_710,plain,
    ld(X0,X0) = rd(X0,X0),
    inference(superposition,[status(thm)],[c_649,c_52]) ).

cnf(c_787,plain,
    ld(mult(X0,X1),mult(X0,X1)) = mult(rd(X0,mult(X1,X0)),X1),
    inference(superposition,[status(thm)],[c_710,c_163]) ).

cnf(c_913,plain,
    ld(mult(X0,X1),mult(X2,X1)) = mult(ld(X1,ld(X0,X2)),X1),
    inference(superposition,[status(thm)],[c_49,c_222]) ).

cnf(c_2895,plain,
    mult(ld(X0,ld(X1,ld(X0,X0))),X0) = ld(mult(X1,X0),X0),
    inference(superposition,[status(thm)],[c_649,c_913]) ).

cnf(c_3330,plain,
    mult(ld(X0,ld(X1,X1)),X0) = mult(rd(X1,mult(X0,X1)),X0),
    inference(demodulation,[status(thm)],[c_787,c_913]) ).

cnf(c_3360,plain,
    rd(mult(ld(X0,ld(X1,X1)),X0),X0) = rd(X1,mult(X0,X1)),
    inference(superposition,[status(thm)],[c_3330,c_52]) ).

cnf(c_7280,plain,
    ld(X0,ld(X1,X1)) = rd(X1,mult(X0,X1)),
    inference(demodulation,[status(thm)],[c_3360,c_52]) ).

cnf(c_7294,plain,
    ld(rd(X0,X1),ld(X1,X1)) = rd(X1,X0),
    inference(superposition,[status(thm)],[c_51,c_7280]) ).

cnf(c_7508,plain,
    rd(ld(X0,X0),rd(X0,X1)) = rd(X1,X0),
    inference(superposition,[status(thm)],[c_7294,c_132]) ).

cnf(c_7513,plain,
    ld(mult(rd(X0,X1),X1),X1) = mult(ld(X1,rd(X1,X0)),X1),
    inference(superposition,[status(thm)],[c_7294,c_2895]) ).

cnf(c_7514,plain,
    mult(ld(X0,rd(X0,X1)),X0) = ld(X1,X0),
    inference(light_normalisation,[status(thm)],[c_7513,c_51]) ).

cnf(c_8305,plain,
    rd(ld(X0,X0),X1) = rd(ld(X1,X0),X0),
    inference(superposition,[status(thm)],[c_132,c_7508]) ).

cnf(c_8496,plain,
    ld(X0,rd(X0,X1)) = rd(ld(X1,X0),X0),
    inference(superposition,[status(thm)],[c_7514,c_52]) ).

cnf(c_9418,plain,
    ld(X0,rd(X0,rd(X0,X1))) = rd(X1,X0),
    inference(superposition,[status(thm)],[c_130,c_8496]) ).

cnf(c_9998,plain,
    ld(X0,rd(X0,X1)) = rd(ld(X0,X0),X1),
    inference(light_normalisation,[status(thm)],[c_8305,c_8496]) ).

cnf(c_10020,plain,
    ld(X0,rd(X0,ld(X1,ld(X0,X0)))) = X1,
    inference(superposition,[status(thm)],[c_9998,c_132]) ).

cnf(c_10034,plain,
    ld(ld(X0,X0),ld(X0,X0)) = ld(X0,rd(X0,ld(X0,X0))),
    inference(superposition,[status(thm)],[c_9998,c_710]) ).

cnf(c_10732,plain,
    ld(X0,rd(X0,ld(X0,X0))) = ld(X0,X0),
    inference(superposition,[status(thm)],[c_710,c_9418]) ).

cnf(c_11510,plain,
    ld(ld(X0,X0),ld(X0,rd(X0,ld(X1,ld(ld(X0,X0),ld(X0,X0)))))) = X1,
    inference(superposition,[status(thm)],[c_9998,c_10020]) ).

cnf(c_11536,plain,
    ld(ld(X0,X0),X1) = X1,
    inference(light_normalisation,[status(thm)],[c_11510,c_10020,c_10034,c_10732]) ).

cnf(c_11611,plain,
    mult(ld(X0,X0),X1) = X1,
    inference(superposition,[status(thm)],[c_11536,c_49]) ).

cnf(c_11615,plain,
    ld(X0,X0) = rd(X1,X1),
    inference(superposition,[status(thm)],[c_11536,c_132]) ).

cnf(c_13343,plain,
    mult(X0,rd(X1,X1)) = X0,
    inference(superposition,[status(thm)],[c_11615,c_49]) ).

cnf(c_13355,plain,
    mult(rd(X0,X0),X1) = X1,
    inference(superposition,[status(thm)],[c_11615,c_11611]) ).

cnf(c_13569,plain,
    mult(rd(X0,X0),sK0(rd(X0,X0))) != sK0(rd(X0,X0)),
    inference(superposition,[status(thm)],[c_13343,c_82]) ).

cnf(c_13850,plain,
    sK0(rd(X0,X0)) != sK0(rd(X0,X0)),
    inference(demodulation,[status(thm)],[c_13569,c_13355]) ).

cnf(c_13851,plain,
    $false,
    inference(equality_resolution_simp,[status(thm)],[c_13850]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : GRP659+1 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.09  % Command  : run_iprover %s %d THM
% 0.09/0.29  % Computer : n024.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 300
% 0.09/0.29  % DateTime : Thu Jun 20 07:59:54 EDT 2024
% 0.09/0.29  % CPUTime  : 
% 0.14/0.39  Running first-order theorem proving
% 0.14/0.39  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.11/2.07  % SZS status Started for theBenchmark.p
% 10.11/2.07  % SZS status Theorem for theBenchmark.p
% 10.11/2.07  
% 10.11/2.07  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 10.11/2.07  
% 10.11/2.07  ------  iProver source info
% 10.11/2.07  
% 10.11/2.07  git: date: 2024-06-12 09:56:46 +0000
% 10.11/2.07  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 10.11/2.07  git: non_committed_changes: false
% 10.11/2.07  
% 10.11/2.07  ------ Parsing...
% 10.11/2.07  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 10.11/2.07  
% 10.11/2.07  ------ Preprocessing... sup_sim: 0  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 10.11/2.07  
% 10.11/2.07  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 10.11/2.07  
% 10.11/2.07  ------ Preprocessing... sf_s  rm: 0 0s  sf_e 
% 10.11/2.07  ------ Proving...
% 10.11/2.07  ------ Problem Properties 
% 10.11/2.07  
% 10.11/2.07  
% 10.11/2.07  clauses                                 6
% 10.11/2.07  conjectures                             1
% 10.11/2.07  EPR                                     0
% 10.11/2.07  Horn                                    6
% 10.11/2.07  unary                                   5
% 10.11/2.07  binary                                  1
% 10.11/2.07  lits                                    7
% 10.11/2.07  lits eq                                 7
% 10.11/2.07  fd_pure                                 0
% 10.11/2.07  fd_pseudo                               0
% 10.11/2.07  fd_cond                                 0
% 10.11/2.07  fd_pseudo_cond                          0
% 10.11/2.07  AC symbols                              0
% 10.11/2.07  
% 10.11/2.07  ------ Schedule dynamic 5 is on 
% 10.11/2.07  
% 10.11/2.07  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.11/2.07  
% 10.11/2.07  
% 10.11/2.07  ------ 
% 10.11/2.07  Current options:
% 10.11/2.07  ------ 
% 10.11/2.07  
% 10.11/2.07  
% 10.11/2.07  
% 10.11/2.07  
% 10.11/2.07  ------ Proving...
% 10.11/2.07  
% 10.11/2.07  
% 10.11/2.07  % SZS status Theorem for theBenchmark.p
% 10.11/2.07  
% 10.11/2.07  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.11/2.07  
% 10.11/2.07  
%------------------------------------------------------------------------------