TSTP Solution File: KLE119+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : KLE119+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n004.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 05:32:10 EDT 2023

% Result   : Theorem 2.61s 1.18s
% Output   : CNFRefutation 2.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   54 (  53 unt;   0 def)
%            Number of atoms       :   55 (  54 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   15 (  14   ~;   0   |;   0   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :   61 (   1 sgn;  45   !;   4   ?)

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

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

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

fof(f17,axiom,
    ! [X3] : zero = multiplication(X3,coantidomain(X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain1) ).

fof(f19,axiom,
    ! [X3] : one = addition(coantidomain(coantidomain(X3)),coantidomain(X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).

fof(f20,axiom,
    ! [X3] : coantidomain(coantidomain(X3)) = codomain(X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain4) ).

fof(f24,axiom,
    ! [X3,X4] : backward_diamond(X3,X4) = codomain(multiplication(codomain(X4),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_diamond) ).

fof(f27,conjecture,
    ! [X3,X4] : domain(X4) = addition(backward_diamond(zero,domain(X3)),domain(X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f28,negated_conjecture,
    ~ ! [X3,X4] : domain(X4) = addition(backward_diamond(zero,domain(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(f33,plain,
    ! [X0] : antidomain(antidomain(X0)) = domain(X0),
    inference(rectify,[],[f16]) ).

fof(f34,plain,
    ! [X0] : zero = multiplication(X0,coantidomain(X0)),
    inference(rectify,[],[f17]) ).

fof(f36,plain,
    ! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
    inference(rectify,[],[f19]) ).

fof(f37,plain,
    ! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
    inference(rectify,[],[f20]) ).

fof(f41,plain,
    ! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
    inference(rectify,[],[f24]) ).

fof(f44,plain,
    ~ ! [X0,X1] : domain(X1) = addition(backward_diamond(zero,domain(X0)),domain(X1)),
    inference(rectify,[],[f28]) ).

fof(f45,plain,
    ? [X0,X1] : domain(X1) != addition(backward_diamond(zero,domain(X0)),domain(X1)),
    inference(ennf_transformation,[],[f44]) ).

fof(f46,plain,
    ( ? [X0,X1] : domain(X1) != addition(backward_diamond(zero,domain(X0)),domain(X1))
   => domain(sK1) != addition(backward_diamond(zero,domain(sK0)),domain(sK1)) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    domain(sK1) != addition(backward_diamond(zero,domain(sK0)),domain(sK1)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[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(f54,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f57,plain,
    ! [X0] : zero = multiplication(X0,zero),
    inference(cnf_transformation,[],[f10]) ).

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

fof(f63,plain,
    ! [X0] : zero = multiplication(X0,coantidomain(X0)),
    inference(cnf_transformation,[],[f34]) ).

fof(f65,plain,
    ! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
    inference(cnf_transformation,[],[f36]) ).

fof(f66,plain,
    ! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
    inference(cnf_transformation,[],[f37]) ).

fof(f70,plain,
    ! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
    inference(cnf_transformation,[],[f41]) ).

fof(f73,plain,
    domain(sK1) != addition(backward_diamond(zero,domain(sK0)),domain(sK1)),
    inference(cnf_transformation,[],[f47]) ).

fof(f75,plain,
    ! [X0,X1] : backward_diamond(X0,X1) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X1)),X0))),
    inference(definition_unfolding,[],[f70,f66,f66]) ).

fof(f80,plain,
    antidomain(antidomain(sK1)) != addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),zero))),antidomain(antidomain(sK1))),
    inference(definition_unfolding,[],[f73,f62,f75,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_55,plain,
    multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f54]) ).

cnf(c_58,plain,
    multiplication(X0,zero) = zero,
    inference(cnf_transformation,[],[f57]) ).

cnf(c_63,plain,
    multiplication(X0,coantidomain(X0)) = zero,
    inference(cnf_transformation,[],[f63]) ).

cnf(c_65,plain,
    addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
    inference(cnf_transformation,[],[f65]) ).

cnf(c_66,negated_conjecture,
    addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),zero))),antidomain(antidomain(sK1))) != antidomain(antidomain(sK1)),
    inference(cnf_transformation,[],[f80]) ).

cnf(c_83,plain,
    addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
    inference(theory_normalisation,[status(thm)],[c_65,c_50,c_49]) ).

cnf(c_84,negated_conjecture,
    addition(antidomain(antidomain(sK1)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),zero)))) != antidomain(antidomain(sK1)),
    inference(theory_normalisation,[status(thm)],[c_66,c_50,c_49]) ).

cnf(c_123,plain,
    addition(antidomain(antidomain(sK1)),coantidomain(coantidomain(zero))) != antidomain(antidomain(sK1)),
    inference(demodulation,[status(thm)],[c_84,c_58]) ).

cnf(c_205,plain,
    addition(coantidomain(coantidomain(zero)),antidomain(antidomain(sK1))) != antidomain(antidomain(sK1)),
    inference(theory_normalisation,[status(thm)],[c_123,c_50,c_49]) ).

cnf(c_208,plain,
    coantidomain(one) = zero,
    inference(superposition,[status(thm)],[c_55,c_63]) ).

cnf(c_210,plain,
    addition(zero,X0) = X0,
    inference(superposition,[status(thm)],[c_51,c_49]) ).

cnf(c_224,plain,
    addition(zero,coantidomain(zero)) = one,
    inference(superposition,[status(thm)],[c_208,c_83]) ).

cnf(c_235,plain,
    coantidomain(zero) = one,
    inference(demodulation,[status(thm)],[c_224,c_210]) ).

cnf(c_236,plain,
    addition(coantidomain(one),antidomain(antidomain(sK1))) != antidomain(antidomain(sK1)),
    inference(demodulation,[status(thm)],[c_205,c_235]) ).

cnf(c_237,plain,
    addition(zero,antidomain(antidomain(sK1))) != antidomain(antidomain(sK1)),
    inference(light_normalisation,[status(thm)],[c_236,c_208]) ).

cnf(c_238,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_237,c_210]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : KLE119+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command  : run_iprover %s %d THM
% 0.15/0.36  % Computer : n004.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Tue Aug 29 11:52:07 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.23/0.50  Running first-order theorem proving
% 0.23/0.50  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.61/1.18  % SZS status Started for theBenchmark.p
% 2.61/1.18  % SZS status Theorem for theBenchmark.p
% 2.61/1.18  
% 2.61/1.18  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.61/1.18  
% 2.61/1.18  ------  iProver source info
% 2.61/1.18  
% 2.61/1.18  git: date: 2023-05-31 18:12:56 +0000
% 2.61/1.18  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.61/1.18  git: non_committed_changes: false
% 2.61/1.18  git: last_make_outside_of_git: false
% 2.61/1.18  
% 2.61/1.18  ------ Parsing...
% 2.61/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.61/1.18  
% 2.61/1.18  ------ Preprocessing... sup_sim: 1  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 2.61/1.18  
% 2.61/1.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.61/1.18  
% 2.61/1.18  ------ Preprocessing... sf_s  rm: 0 0s  sf_e 
% 2.61/1.18  ------ Proving...
% 2.61/1.18  ------ Problem Properties 
% 2.61/1.18  
% 2.61/1.18  
% 2.61/1.18  clauses                                 18
% 2.61/1.18  conjectures                             0
% 2.61/1.18  EPR                                     0
% 2.61/1.18  Horn                                    18
% 2.61/1.18  unary                                   18
% 2.61/1.18  binary                                  0
% 2.61/1.18  lits                                    18
% 2.61/1.18  lits eq                                 18
% 2.61/1.18  fd_pure                                 0
% 2.61/1.18  fd_pseudo                               0
% 2.61/1.18  fd_cond                                 0
% 2.61/1.18  fd_pseudo_cond                          0
% 2.61/1.18  AC symbols                              1
% 2.61/1.18  
% 2.61/1.18  ------ Schedule UEQ
% 2.61/1.18  
% 2.61/1.18  ------ Option_UEQ Time Limit: 10.
% 2.61/1.18  
% 2.61/1.18  
% 2.61/1.18  ------ 
% 2.61/1.18  Current options:
% 2.61/1.18  ------ 
% 2.61/1.18  
% 2.61/1.18  
% 2.61/1.18  
% 2.61/1.18  
% 2.61/1.18  ------ Proving...
% 2.61/1.18  
% 2.61/1.18  
% 2.61/1.18  % SZS status Theorem for theBenchmark.p
% 2.61/1.18  
% 2.61/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.61/1.18  
% 2.61/1.18  
%------------------------------------------------------------------------------