TSTP Solution File: KLE131+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : KLE131+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n025.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 05:32:12 EDT 2023

% Result   : Theorem 3.83s 1.14s
% Output   : CNFRefutation 3.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   60 (  54 unt;   0 def)
%            Number of atoms       :   68 (  67 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   16 (   8   ~;   0   |;   4   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :   16 (   3 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-2 aty)
%            Number of variables   :   77 (   1 sgn;  60   !;   2   ?)

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

fof(f2,axiom,
    ! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).

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

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).

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

fof(f13,axiom,
    ! [X3] : zero = multiplication(antidomain(X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).

fof(f15,axiom,
    ! [X3] : one = addition(antidomain(antidomain(X3)),antidomain(X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).

fof(f16,axiom,
    ! [X3] : antidomain(antidomain(X3)) = domain(X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).

fof(f22,axiom,
    ! [X3,X4] : domain_difference(X3,X4) = multiplication(domain(X3),antidomain(X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_difference) ).

fof(f23,axiom,
    ! [X3,X4] : forward_diamond(X3,X4) = domain(multiplication(X3,domain(X4))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).

fof(f27,axiom,
    ! [X3] : divergence(X3) = forward_diamond(X3,divergence(X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence1) ).

fof(f29,conjecture,
    ! [X3] :
      ( ! [X4] : forward_diamond(star(X3),domain_difference(domain(X4),forward_diamond(X3,domain(X4)))) = addition(domain(X4),forward_diamond(star(X3),domain_difference(domain(X4),forward_diamond(X3,domain(X4)))))
     => zero = divergence(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f30,negated_conjecture,
    ~ ! [X3] :
        ( ! [X4] : forward_diamond(star(X3),domain_difference(domain(X4),forward_diamond(X3,domain(X4)))) = addition(domain(X4),forward_diamond(star(X3),domain_difference(domain(X4),forward_diamond(X3,domain(X4)))))
       => zero = divergence(X3) ),
    inference(negated_conjecture,[],[f29]) ).

fof(f31,plain,
    ! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(rectify,[],[f2]) ).

fof(f32,plain,
    ! [X0] : zero = multiplication(antidomain(X0),X0),
    inference(rectify,[],[f13]) ).

fof(f34,plain,
    ! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
    inference(rectify,[],[f15]) ).

fof(f35,plain,
    ! [X0] : antidomain(antidomain(X0)) = domain(X0),
    inference(rectify,[],[f16]) ).

fof(f41,plain,
    ! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
    inference(rectify,[],[f22]) ).

fof(f42,plain,
    ! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
    inference(rectify,[],[f23]) ).

fof(f46,plain,
    ! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
    inference(rectify,[],[f27]) ).

fof(f48,plain,
    ~ ! [X0] :
        ( ! [X1] : forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) = addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))))
       => zero = divergence(X0) ),
    inference(rectify,[],[f30]) ).

fof(f50,plain,
    ? [X0] :
      ( zero != divergence(X0)
      & ! [X1] : forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) = addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f51,plain,
    ( ? [X0] :
        ( zero != divergence(X0)
        & ! [X1] : forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) = addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) )
   => ( zero != divergence(sK0)
      & ! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ( zero != divergence(sK0)
    & ! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f50,f51]) ).

fof(f53,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f54,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f31]) ).

fof(f55,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f58,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f62,plain,
    ! [X0] : zero = multiplication(X0,zero),
    inference(cnf_transformation,[],[f10]) ).

fof(f64,plain,
    ! [X0] : zero = multiplication(antidomain(X0),X0),
    inference(cnf_transformation,[],[f32]) ).

fof(f66,plain,
    ! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
    inference(cnf_transformation,[],[f34]) ).

fof(f67,plain,
    ! [X0] : antidomain(antidomain(X0)) = domain(X0),
    inference(cnf_transformation,[],[f35]) ).

fof(f73,plain,
    ! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
    inference(cnf_transformation,[],[f41]) ).

fof(f74,plain,
    ! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
    inference(cnf_transformation,[],[f42]) ).

fof(f78,plain,
    ! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
    inference(cnf_transformation,[],[f46]) ).

fof(f80,plain,
    ! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))),
    inference(cnf_transformation,[],[f52]) ).

fof(f81,plain,
    zero != divergence(sK0),
    inference(cnf_transformation,[],[f52]) ).

fof(f85,plain,
    ! [X0,X1] : domain_difference(X0,X1) = multiplication(antidomain(antidomain(X0)),antidomain(X1)),
    inference(definition_unfolding,[],[f73,f67]) ).

fof(f86,plain,
    ! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
    inference(definition_unfolding,[],[f74,f67,f67]) ).

fof(f88,plain,
    ! [X0] : divergence(X0) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))),
    inference(definition_unfolding,[],[f78,f86]) ).

fof(f90,plain,
    ! [X1] : antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1)))))))))))))) = addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))))))))))),
    inference(definition_unfolding,[],[f80,f86,f85,f67,f86,f67,f67,f86,f85,f67,f86,f67]) ).

cnf(c_49,plain,
    addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_50,plain,
    addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_51,plain,
    addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f55]) ).

cnf(c_54,plain,
    multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f58]) ).

cnf(c_58,plain,
    multiplication(X0,zero) = zero,
    inference(cnf_transformation,[],[f62]) ).

cnf(c_60,plain,
    multiplication(antidomain(X0),X0) = zero,
    inference(cnf_transformation,[],[f64]) ).

cnf(c_62,plain,
    addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
    inference(cnf_transformation,[],[f66]) ).

cnf(c_66,plain,
    antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))) = divergence(X0),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_68,negated_conjecture,
    divergence(sK0) != zero,
    inference(cnf_transformation,[],[f81]) ).

cnf(c_69,negated_conjecture,
    addition(antidomain(antidomain(X0)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X0)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X0)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0)))))))))))))),
    inference(cnf_transformation,[],[f90]) ).

cnf(c_88,plain,
    addition(antidomain(X0),antidomain(antidomain(X0))) = one,
    inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).

cnf(c_243,plain,
    antidomain(one) = zero,
    inference(superposition,[status(thm)],[c_54,c_60]) ).

cnf(c_247,plain,
    addition(zero,X0) = X0,
    inference(superposition,[status(thm)],[c_51,c_49]) ).

cnf(c_252,plain,
    addition(zero,antidomain(zero)) = one,
    inference(superposition,[status(thm)],[c_243,c_88]) ).

cnf(c_260,plain,
    antidomain(zero) = one,
    inference(demodulation,[status(thm)],[c_252,c_247]) ).

cnf(c_568,plain,
    addition(divergence(X0),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(X0))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(X0))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0))))))))))))),
    inference(superposition,[status(thm)],[c_66,c_69]) ).

cnf(c_882,plain,
    addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(sK0))),antidomain(divergence(sK0))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(sK0))),antidomain(divergence(sK0)))))))),
    inference(superposition,[status(thm)],[c_66,c_568]) ).

cnf(c_1049,plain,
    divergence(sK0) = zero,
    inference(demodulation,[status(thm)],[c_882,c_51,c_58,c_60,c_243,c_260]) ).

cnf(c_1050,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1049,c_68]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : KLE131+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n025.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 : Tue Aug 29 11:38:10 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.83/1.14  % SZS status Started for theBenchmark.p
% 3.83/1.14  % SZS status Theorem for theBenchmark.p
% 3.83/1.14  
% 3.83/1.14  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.83/1.14  
% 3.83/1.14  ------  iProver source info
% 3.83/1.14  
% 3.83/1.14  git: date: 2023-05-31 18:12:56 +0000
% 3.83/1.14  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.83/1.14  git: non_committed_changes: false
% 3.83/1.14  git: last_make_outside_of_git: false
% 3.83/1.14  
% 3.83/1.14  ------ Parsing...
% 3.83/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.83/1.14  
% 3.83/1.14  ------ Preprocessing... sup_sim: 0  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 3.83/1.14  
% 3.83/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.83/1.14  
% 3.83/1.14  ------ Preprocessing... sf_s  rm: 0 0s  sf_e 
% 3.83/1.14  ------ Proving...
% 3.83/1.14  ------ Problem Properties 
% 3.83/1.14  
% 3.83/1.14  
% 3.83/1.14  clauses                                 21
% 3.83/1.14  conjectures                             2
% 3.83/1.14  EPR                                     0
% 3.83/1.14  Horn                                    21
% 3.83/1.14  unary                                   20
% 3.83/1.14  binary                                  1
% 3.83/1.14  lits                                    22
% 3.83/1.14  lits eq                                 22
% 3.83/1.14  fd_pure                                 0
% 3.83/1.14  fd_pseudo                               0
% 3.83/1.14  fd_cond                                 0
% 3.83/1.14  fd_pseudo_cond                          0
% 3.83/1.14  AC symbols                              1
% 3.83/1.14  
% 3.83/1.14  ------ Schedule dynamic 5 is on 
% 3.83/1.14  
% 3.83/1.14  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.83/1.14  
% 3.83/1.14  
% 3.83/1.14  ------ 
% 3.83/1.14  Current options:
% 3.83/1.14  ------ 
% 3.83/1.14  
% 3.83/1.14  
% 3.83/1.14  
% 3.83/1.14  
% 3.83/1.14  ------ Proving...
% 3.83/1.14  
% 3.83/1.14  
% 3.83/1.14  % SZS status Theorem for theBenchmark.p
% 3.83/1.14  
% 3.83/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.83/1.14  
% 3.83/1.15  
%------------------------------------------------------------------------------