TSTP Solution File: LCL456+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : LCL456+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 07:44:35 EDT 2023

% Result   : Theorem 3.99s 1.15s
% Output   : CNFRefutation 3.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   64 (  35 unt;   0 def)
%            Number of atoms       :   93 (  24 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   55 (  26   ~;  19   |;   0   &)
%                                         (   3 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    9 (   7 usr;   7 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   80 (   0 sgn;  38   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ( modus_tollens
  <=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).

fof(f24,axiom,
    ( r3
  <=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).

fof(f27,axiom,
    ( op_or
   => ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).

fof(f28,axiom,
    ( op_and
   => ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).

fof(f29,axiom,
    ( op_implies_and
   => ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).

fof(f30,axiom,
    ( op_implies_or
   => ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).

fof(f32,axiom,
    op_or,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).

fof(f33,axiom,
    op_implies_and,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).

fof(f36,axiom,
    modus_tollens,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).

fof(f50,axiom,
    op_implies_or,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).

fof(f51,axiom,
    op_and,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).

fof(f53,conjecture,
    r3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).

fof(f54,negated_conjecture,
    ~ r3,
    inference(negated_conjecture,[],[f53]) ).

fof(f63,plain,
    ( r3
  <=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(rectify,[],[f24]) ).

fof(f66,plain,
    ~ r3,
    inference(flattening,[],[f54]) ).

fof(f67,plain,
    ( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
   => r3 ),
    inference(unused_predicate_definition_removal,[],[f63]) ).

fof(f80,plain,
    ( modus_tollens
   => ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f3]) ).

fof(f86,plain,
    ( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
    | ~ modus_tollens ),
    inference(ennf_transformation,[],[f80]) ).

fof(f99,plain,
    ( r3
    | ? [X0,X1] : ~ is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f100,plain,
    ( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
    | ~ op_or ),
    inference(ennf_transformation,[],[f27]) ).

fof(f101,plain,
    ( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
    | ~ op_and ),
    inference(ennf_transformation,[],[f28]) ).

fof(f102,plain,
    ( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
    | ~ op_implies_and ),
    inference(ennf_transformation,[],[f29]) ).

fof(f103,plain,
    ( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
    | ~ op_implies_or ),
    inference(ennf_transformation,[],[f30]) ).

fof(f105,plain,
    ( ? [X0,X1] : ~ is_a_theorem(implies(or(X0,X1),or(X1,X0)))
   => ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ),
    introduced(choice_axiom,[]) ).

fof(f106,plain,
    ( r3
    | ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f99,f105]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
      | ~ modus_tollens ),
    inference(cnf_transformation,[],[f86]) ).

fof(f122,plain,
    ( r3
    | ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( or(X0,X1) = not(and(not(X0),not(X1)))
      | ~ op_or ),
    inference(cnf_transformation,[],[f100]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( and(X0,X1) = not(or(not(X0),not(X1)))
      | ~ op_and ),
    inference(cnf_transformation,[],[f101]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = not(and(X0,not(X1)))
      | ~ op_implies_and ),
    inference(cnf_transformation,[],[f102]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = or(not(X0),X1)
      | ~ op_implies_or ),
    inference(cnf_transformation,[],[f103]) ).

fof(f128,plain,
    op_or,
    inference(cnf_transformation,[],[f32]) ).

fof(f129,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f33]) ).

fof(f132,plain,
    modus_tollens,
    inference(cnf_transformation,[],[f36]) ).

fof(f146,plain,
    op_implies_or,
    inference(cnf_transformation,[],[f50]) ).

fof(f147,plain,
    op_and,
    inference(cnf_transformation,[],[f51]) ).

fof(f149,plain,
    ~ r3,
    inference(cnf_transformation,[],[f66]) ).

cnf(c_51,plain,
    ( ~ modus_tollens
    | is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
    inference(cnf_transformation,[],[f109]) ).

cnf(c_64,plain,
    ( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))
    | r3 ),
    inference(cnf_transformation,[],[f122]) ).

cnf(c_65,plain,
    ( ~ op_or
    | not(and(not(X0),not(X1))) = or(X0,X1) ),
    inference(cnf_transformation,[],[f123]) ).

cnf(c_66,plain,
    ( ~ op_and
    | not(or(not(X0),not(X1))) = and(X0,X1) ),
    inference(cnf_transformation,[],[f124]) ).

cnf(c_67,plain,
    ( ~ op_implies_and
    | not(and(X0,not(X1))) = implies(X0,X1) ),
    inference(cnf_transformation,[],[f125]) ).

cnf(c_68,plain,
    ( ~ op_implies_or
    | or(not(X0),X1) = implies(X0,X1) ),
    inference(cnf_transformation,[],[f126]) ).

cnf(c_70,plain,
    op_or,
    inference(cnf_transformation,[],[f128]) ).

cnf(c_71,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f129]) ).

cnf(c_74,plain,
    modus_tollens,
    inference(cnf_transformation,[],[f132]) ).

cnf(c_88,plain,
    op_implies_or,
    inference(cnf_transformation,[],[f146]) ).

cnf(c_89,plain,
    op_and,
    inference(cnf_transformation,[],[f147]) ).

cnf(c_91,negated_conjecture,
    ~ r3,
    inference(cnf_transformation,[],[f149]) ).

cnf(c_124,plain,
    ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))),
    inference(global_subsumption_just,[status(thm)],[c_64,c_91,c_64]) ).

cnf(c_134,plain,
    or(not(X0),X1) = implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_68,c_88,c_68]) ).

cnf(c_140,plain,
    not(and(X0,not(X1))) = implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_67,c_71,c_67]) ).

cnf(c_146,plain,
    is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
    inference(global_subsumption_just,[status(thm)],[c_51,c_74,c_51]) ).

cnf(c_151,plain,
    not(or(not(X0),not(X1))) = and(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_66,c_89,c_66]) ).

cnf(c_154,plain,
    not(and(not(X0),not(X1))) = or(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_65,c_70,c_65]) ).

cnf(c_512,plain,
    not(implies(X0,not(X1))) = and(X0,X1),
    inference(demodulation,[status(thm)],[c_151,c_134]) ).

cnf(c_516,plain,
    implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
    inference(superposition,[status(thm)],[c_512,c_134]) ).

cnf(c_541,plain,
    is_a_theorem(or(and(not(X0),X1),implies(X1,X0))),
    inference(demodulation,[status(thm)],[c_146,c_516]) ).

cnf(c_615,plain,
    implies(not(X0),X1) = or(X0,X1),
    inference(demodulation,[status(thm)],[c_154,c_140]) ).

cnf(c_617,plain,
    or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
    inference(superposition,[status(thm)],[c_140,c_615]) ).

cnf(c_1576,plain,
    is_a_theorem(implies(implies(not(X0),X1),implies(not(X1),X0))),
    inference(superposition,[status(thm)],[c_617,c_541]) ).

cnf(c_1580,plain,
    is_a_theorem(implies(or(X0,X1),implies(not(X1),X0))),
    inference(light_normalisation,[status(thm)],[c_1576,c_615]) ).

cnf(c_1581,plain,
    is_a_theorem(implies(or(X0,X1),or(X1,X0))),
    inference(demodulation,[status(thm)],[c_1580,c_615]) ).

cnf(c_1592,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_124,c_1581]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL456+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Aug 25 01:14:40 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.99/1.15  % SZS status Started for theBenchmark.p
% 3.99/1.15  % SZS status Theorem for theBenchmark.p
% 3.99/1.15  
% 3.99/1.15  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.99/1.15  
% 3.99/1.15  ------  iProver source info
% 3.99/1.15  
% 3.99/1.15  git: date: 2023-05-31 18:12:56 +0000
% 3.99/1.15  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.99/1.15  git: non_committed_changes: false
% 3.99/1.15  git: last_make_outside_of_git: false
% 3.99/1.15  
% 3.99/1.15  ------ Parsing...
% 3.99/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.99/1.15  
% 3.99/1.15  ------ Preprocessing... sup_sim: 0  sf_s  rm: 22 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.99/1.15  
% 3.99/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.99/1.15  
% 3.99/1.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.99/1.15  ------ Proving...
% 3.99/1.15  ------ Problem Properties 
% 3.99/1.15  
% 3.99/1.15  
% 3.99/1.15  clauses                                 21
% 3.99/1.15  conjectures                             0
% 3.99/1.15  EPR                                     0
% 3.99/1.15  Horn                                    21
% 3.99/1.15  unary                                   19
% 3.99/1.15  binary                                  1
% 3.99/1.15  lits                                    24
% 3.99/1.15  lits eq                                 6
% 3.99/1.15  fd_pure                                 0
% 3.99/1.15  fd_pseudo                               0
% 3.99/1.15  fd_cond                                 0
% 3.99/1.15  fd_pseudo_cond                          1
% 3.99/1.15  AC symbols                              0
% 3.99/1.15  
% 3.99/1.15  ------ Input Options Time Limit: Unbounded
% 3.99/1.15  
% 3.99/1.15  
% 3.99/1.15  ------ 
% 3.99/1.15  Current options:
% 3.99/1.15  ------ 
% 3.99/1.15  
% 3.99/1.15  
% 3.99/1.15  
% 3.99/1.15  
% 3.99/1.15  ------ Proving...
% 3.99/1.15  
% 3.99/1.15  
% 3.99/1.15  % SZS status Theorem for theBenchmark.p
% 3.99/1.15  
% 3.99/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.99/1.15  
% 3.99/1.15  
%------------------------------------------------------------------------------