TSTP Solution File: KLE099+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : KLE099+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n010.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 05:32:07 EDT 2023

% Result   : Theorem 18.87s 3.70s
% Output   : CNFRefutation 18.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   83 (  77 unt;   0 def)
%            Number of atoms       :   91 (  90 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   17 (   9   ~;   0   |;   4   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :  130 (  10 sgn;  67   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).

fof(f2,axiom,
    ! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).

fof(f3,axiom,
    ! [X0] : addition(X0,zero) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).

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

fof(f5,axiom,
    ! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).

fof(f7,axiom,
    ! [X0] : multiplication(one,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).

fof(f8,axiom,
    ! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).

fof(f9,axiom,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).

fof(f11,axiom,
    ! [X0] : zero = multiplication(zero,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).

fof(f13,axiom,
    ! [X3] : zero = multiplication(antidomain(X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).

fof(f15,axiom,
    ! [X3] : one = addition(antidomain(antidomain(X3)),antidomain(X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).

fof(f16,axiom,
    ! [X3] : antidomain(antidomain(X3)) = domain(X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).

fof(f23,axiom,
    ! [X3,X4] : forward_diamond(X3,X4) = domain(multiplication(X3,domain(X4))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_diamond) ).

fof(f27,conjecture,
    ! [X3,X4,X5] :
      ( domain(X5) = addition(forward_diamond(X3,domain(X4)),domain(X5))
     => zero = multiplication(antidomain(X5),multiplication(X3,domain(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f28,negated_conjecture,
    ~ ! [X3,X4,X5] :
        ( domain(X5) = addition(forward_diamond(X3,domain(X4)),domain(X5))
       => zero = multiplication(antidomain(X5),multiplication(X3,domain(X4))) ),
    inference(negated_conjecture,[],[f27]) ).

fof(f29,plain,
    ! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(rectify,[],[f2]) ).

fof(f30,plain,
    ! [X0] : zero = multiplication(antidomain(X0),X0),
    inference(rectify,[],[f13]) ).

fof(f32,plain,
    ! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
    inference(rectify,[],[f15]) ).

fof(f33,plain,
    ! [X0] : antidomain(antidomain(X0)) = domain(X0),
    inference(rectify,[],[f16]) ).

fof(f40,plain,
    ! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
    inference(rectify,[],[f23]) ).

fof(f44,plain,
    ~ ! [X0,X1,X2] :
        ( domain(X2) = addition(forward_diamond(X0,domain(X1)),domain(X2))
       => zero = multiplication(antidomain(X2),multiplication(X0,domain(X1))) ),
    inference(rectify,[],[f28]) ).

fof(f45,plain,
    ? [X0,X1,X2] :
      ( zero != multiplication(antidomain(X2),multiplication(X0,domain(X1)))
      & domain(X2) = addition(forward_diamond(X0,domain(X1)),domain(X2)) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f46,plain,
    ( ? [X0,X1,X2] :
        ( zero != multiplication(antidomain(X2),multiplication(X0,domain(X1)))
        & domain(X2) = addition(forward_diamond(X0,domain(X1)),domain(X2)) )
   => ( zero != multiplication(antidomain(sK2),multiplication(sK0,domain(sK1)))
      & domain(sK2) = addition(forward_diamond(sK0,domain(sK1)),domain(sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ( zero != multiplication(antidomain(sK2),multiplication(sK0,domain(sK1)))
    & domain(sK2) = addition(forward_diamond(sK0,domain(sK1)),domain(sK2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f45,f46]) ).

fof(f48,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f49,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f29]) ).

fof(f50,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f51,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f52,plain,
    ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(cnf_transformation,[],[f5]) ).

fof(f53,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f54,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f55,plain,
    ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    inference(cnf_transformation,[],[f8]) ).

fof(f56,plain,
    ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[],[f9]) ).

fof(f58,plain,
    ! [X0] : zero = multiplication(zero,X0),
    inference(cnf_transformation,[],[f11]) ).

fof(f59,plain,
    ! [X0] : zero = multiplication(antidomain(X0),X0),
    inference(cnf_transformation,[],[f30]) ).

fof(f61,plain,
    ! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
    inference(cnf_transformation,[],[f32]) ).

fof(f62,plain,
    ! [X0] : antidomain(antidomain(X0)) = domain(X0),
    inference(cnf_transformation,[],[f33]) ).

fof(f69,plain,
    ! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
    inference(cnf_transformation,[],[f40]) ).

fof(f73,plain,
    domain(sK2) = addition(forward_diamond(sK0,domain(sK1)),domain(sK2)),
    inference(cnf_transformation,[],[f47]) ).

fof(f74,plain,
    zero != multiplication(antidomain(sK2),multiplication(sK0,domain(sK1))),
    inference(cnf_transformation,[],[f47]) ).

fof(f79,plain,
    ! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
    inference(definition_unfolding,[],[f69,f62,f62]) ).

fof(f81,plain,
    zero != multiplication(antidomain(sK2),multiplication(sK0,antidomain(antidomain(sK1)))),
    inference(definition_unfolding,[],[f74,f62]) ).

fof(f82,plain,
    antidomain(antidomain(sK2)) = addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))),
    inference(definition_unfolding,[],[f73,f62,f79,f62,f62]) ).

cnf(c_49,plain,
    addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_50,plain,
    addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_51,plain,
    addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f50]) ).

cnf(c_52,plain,
    addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f51]) ).

cnf(c_53,plain,
    multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_54,plain,
    multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f53]) ).

cnf(c_55,plain,
    multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f54]) ).

cnf(c_56,plain,
    addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_57,plain,
    addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_59,plain,
    multiplication(zero,X0) = zero,
    inference(cnf_transformation,[],[f58]) ).

cnf(c_60,plain,
    multiplication(antidomain(X0),X0) = zero,
    inference(cnf_transformation,[],[f59]) ).

cnf(c_62,plain,
    addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
    inference(cnf_transformation,[],[f61]) ).

cnf(c_66,negated_conjecture,
    multiplication(antidomain(sK2),multiplication(sK0,antidomain(antidomain(sK1)))) != zero,
    inference(cnf_transformation,[],[f81]) ).

cnf(c_67,negated_conjecture,
    addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),antidomain(antidomain(sK2))) = antidomain(antidomain(sK2)),
    inference(cnf_transformation,[],[f82]) ).

cnf(c_83,plain,
    addition(antidomain(X0),antidomain(antidomain(X0))) = one,
    inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).

cnf(c_85,negated_conjecture,
    addition(antidomain(antidomain(sK2)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1)))))))) = antidomain(antidomain(sK2)),
    inference(theory_normalisation,[status(thm)],[c_67,c_50,c_49]) ).

cnf(c_213,plain,
    addition(zero,X0) = X0,
    inference(superposition,[status(thm)],[c_51,c_49]) ).

cnf(c_236,plain,
    addition(X0,addition(X0,X1)) = addition(X0,X1),
    inference(superposition,[status(thm)],[c_52,c_50]) ).

cnf(c_365,plain,
    addition(multiplication(X0,antidomain(X1)),multiplication(X0,antidomain(antidomain(X1)))) = multiplication(X0,one),
    inference(superposition,[status(thm)],[c_83,c_56]) ).

cnf(c_378,plain,
    addition(multiplication(antidomain(addition(X0,X1)),X0),multiplication(antidomain(addition(X0,X1)),X1)) = zero,
    inference(superposition,[status(thm)],[c_56,c_60]) ).

cnf(c_388,plain,
    addition(multiplication(X0,antidomain(X1)),multiplication(X0,antidomain(antidomain(X1)))) = X0,
    inference(light_normalisation,[status(thm)],[c_365,c_54]) ).

cnf(c_401,plain,
    addition(multiplication(antidomain(X0),X1),multiplication(antidomain(antidomain(X0)),X1)) = multiplication(one,X1),
    inference(superposition,[status(thm)],[c_83,c_57]) ).

cnf(c_3404,plain,
    addition(multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0)),zero) = antidomain(antidomain(antidomain(X0))),
    inference(superposition,[status(thm)],[c_60,c_388]) ).

cnf(c_3421,plain,
    addition(zero,multiplication(antidomain(antidomain(antidomain(X0))),antidomain(X0))) = antidomain(antidomain(antidomain(X0))),
    inference(theory_normalisation,[status(thm)],[c_3404,c_50,c_49]) ).

cnf(c_11556,plain,
    addition(multiplication(antidomain(addition(X0,X1)),X0),zero) = zero,
    inference(superposition,[status(thm)],[c_378,c_236]) ).

cnf(c_11589,plain,
    addition(zero,multiplication(antidomain(addition(X0,X1)),X0)) = zero,
    inference(theory_normalisation,[status(thm)],[c_11556,c_50,c_49]) ).

cnf(c_12808,plain,
    addition(multiplication(antidomain(X0),X1),multiplication(antidomain(antidomain(X0)),X1)) = X1,
    inference(demodulation,[status(thm)],[c_401,c_55]) ).

cnf(c_12812,plain,
    addition(zero,multiplication(antidomain(antidomain(X0)),X0)) = X0,
    inference(superposition,[status(thm)],[c_60,c_12808]) ).

cnf(c_13327,plain,
    multiplication(antidomain(antidomain(X0)),X0) = X0,
    inference(demodulation,[status(thm)],[c_12812,c_213]) ).

cnf(c_14348,plain,
    multiplication(antidomain(addition(X0,X1)),X0) = zero,
    inference(demodulation,[status(thm)],[c_11589,c_213]) ).

cnf(c_14508,plain,
    multiplication(antidomain(addition(X0,X1)),multiplication(X0,X2)) = multiplication(zero,X2),
    inference(superposition,[status(thm)],[c_14348,c_53]) ).

cnf(c_18631,plain,
    multiplication(antidomain(addition(X0,X1)),multiplication(X0,X2)) = zero,
    inference(demodulation,[status(thm)],[c_14508,c_59]) ).

cnf(c_18639,plain,
    multiplication(antidomain(addition(X0,X1)),multiplication(X1,X2)) = zero,
    inference(superposition,[status(thm)],[c_49,c_18631]) ).

cnf(c_19149,plain,
    multiplication(antidomain(addition(X0,antidomain(antidomain(X1)))),X1) = zero,
    inference(superposition,[status(thm)],[c_13327,c_18639]) ).

cnf(c_77450,plain,
    antidomain(antidomain(antidomain(X0))) = antidomain(X0),
    inference(demodulation,[status(thm)],[c_3421,c_12812]) ).

cnf(c_77640,plain,
    addition(antidomain(antidomain(sK2)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(sK1)))))) = antidomain(antidomain(sK2)),
    inference(demodulation,[status(thm)],[c_85,c_77450]) ).

cnf(c_77935,plain,
    multiplication(antidomain(antidomain(antidomain(sK2))),multiplication(sK0,antidomain(antidomain(sK1)))) = zero,
    inference(superposition,[status(thm)],[c_77640,c_19149]) ).

cnf(c_77953,plain,
    multiplication(antidomain(sK2),multiplication(sK0,antidomain(antidomain(sK1)))) = zero,
    inference(demodulation,[status(thm)],[c_77935,c_77450]) ).

cnf(c_77954,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_77953,c_66]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : KLE099+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.34  % Computer : n010.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue Aug 29 12:14:19 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.21/0.46  Running first-order theorem proving
% 0.21/0.46  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 18.87/3.70  % SZS status Started for theBenchmark.p
% 18.87/3.70  % SZS status Theorem for theBenchmark.p
% 18.87/3.70  
% 18.87/3.70  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 18.87/3.70  
% 18.87/3.70  ------  iProver source info
% 18.87/3.70  
% 18.87/3.70  git: date: 2023-05-31 18:12:56 +0000
% 18.87/3.70  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 18.87/3.70  git: non_committed_changes: false
% 18.87/3.70  git: last_make_outside_of_git: false
% 18.87/3.70  
% 18.87/3.70  ------ Parsing...
% 18.87/3.70  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 18.87/3.70  
% 18.87/3.70  ------ Preprocessing... sup_sim: 0  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 18.87/3.70  
% 18.87/3.70  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 18.87/3.70  
% 18.87/3.70  ------ Preprocessing... sf_s  rm: 0 0s  sf_e 
% 18.87/3.70  ------ Proving...
% 18.87/3.70  ------ Problem Properties 
% 18.87/3.70  
% 18.87/3.70  
% 18.87/3.70  clauses                                 19
% 18.87/3.70  conjectures                             2
% 18.87/3.70  EPR                                     0
% 18.87/3.70  Horn                                    19
% 18.87/3.70  unary                                   19
% 18.87/3.70  binary                                  0
% 18.87/3.70  lits                                    19
% 18.87/3.70  lits eq                                 19
% 18.87/3.70  fd_pure                                 0
% 18.87/3.70  fd_pseudo                               0
% 18.87/3.70  fd_cond                                 0
% 18.87/3.70  fd_pseudo_cond                          0
% 18.87/3.70  AC symbols                              1
% 18.87/3.70  
% 18.87/3.70  ------ Schedule UEQ
% 18.87/3.70  
% 18.87/3.70  ------ Option_UEQ Time Limit: 10.
% 18.87/3.70  
% 18.87/3.70  
% 18.87/3.70  ------ 
% 18.87/3.70  Current options:
% 18.87/3.70  ------ 
% 18.87/3.70  
% 18.87/3.70  
% 18.87/3.70  
% 18.87/3.70  
% 18.87/3.70  ------ Proving...
% 18.87/3.70  
% 18.87/3.70  
% 18.87/3.70  % SZS status Theorem for theBenchmark.p
% 18.87/3.70  
% 18.87/3.70  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.87/3.70  
% 18.87/3.70  
%------------------------------------------------------------------------------