TSTP Solution File: KLE174+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : KLE174+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 05:32:24 EDT 2023

% Result   : Satisfiable 1.29s 1.18s
% Output   : Saturation 1.29s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% 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(f10,axiom,
    ! [X0] : zero = multiplication(X0,zero),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).

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(f14,axiom,
    ! [X3,X4] : antidomain(multiplication(X3,antidomain(antidomain(X4)))) = addition(antidomain(multiplication(X3,X4)),antidomain(multiplication(X3,antidomain(antidomain(X4))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).

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(f17,axiom,
    ! [X3] : zero = multiplication(X3,coantidomain(X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain1) ).

fof(f18,axiom,
    ! [X3,X4] : coantidomain(multiplication(coantidomain(coantidomain(X3)),X4)) = addition(coantidomain(multiplication(X3,X4)),coantidomain(multiplication(coantidomain(coantidomain(X3)),X4))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain2) ).

fof(f19,axiom,
    ! [X3] : one = addition(coantidomain(coantidomain(X3)),coantidomain(X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain3) ).

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,axiom,
    ! [X3] : divergence(X3) = forward_diamond(X3,divergence(X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divergence1) ).

fof(f28,axiom,
    ! [X3,X4,X5] :
      ( addition(forward_diamond(X4,domain(X3)),domain(X5)) = addition(domain(X3),addition(forward_diamond(X4,domain(X3)),domain(X5)))
     => addition(divergence(X4),forward_diamond(star(X4),domain(X5))) = addition(domain(X3),addition(divergence(X4),forward_diamond(star(X4),domain(X5)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divergence2) ).

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(f31,plain,
    ! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
    inference(rectify,[],[f14]) ).

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

fof(f35,plain,
    ! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
    inference(rectify,[],[f18]) ).

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

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

fof(f44,plain,
    ! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
    inference(rectify,[],[f27]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( addition(forward_diamond(X1,domain(X0)),domain(X2)) = addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2)))
     => addition(divergence(X1),forward_diamond(star(X1),domain(X2))) = addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) ),
    inference(rectify,[],[f28]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( addition(divergence(X1),forward_diamond(star(X1),domain(X2))) = addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2))))
      | addition(forward_diamond(X1,domain(X0)),domain(X2)) != addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f47,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f48,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f29]) ).

fof(f49,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f50,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f51,plain,
    ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(cnf_transformation,[],[f5]) ).

fof(f52,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f53,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f54,plain,
    ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    inference(cnf_transformation,[],[f8]) ).

fof(f55,plain,
    ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[],[f9]) ).

fof(f56,plain,
    ! [X0] : zero = multiplication(X0,zero),
    inference(cnf_transformation,[],[f10]) ).

fof(f57,plain,
    ! [X0] : zero = multiplication(zero,X0),
    inference(cnf_transformation,[],[f11]) ).

fof(f58,plain,
    ! [X0] : zero = multiplication(antidomain(X0),X0),
    inference(cnf_transformation,[],[f30]) ).

fof(f59,plain,
    ! [X0,X1] : antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))),
    inference(cnf_transformation,[],[f31]) ).

fof(f60,plain,
    ! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
    inference(cnf_transformation,[],[f32]) ).

fof(f61,plain,
    ! [X0] : antidomain(antidomain(X0)) = domain(X0),
    inference(cnf_transformation,[],[f33]) ).

fof(f62,plain,
    ! [X0] : zero = multiplication(X0,coantidomain(X0)),
    inference(cnf_transformation,[],[f34]) ).

fof(f63,plain,
    ! [X0,X1] : coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))),
    inference(cnf_transformation,[],[f35]) ).

fof(f64,plain,
    ! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
    inference(cnf_transformation,[],[f36]) ).

fof(f68,plain,
    ! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
    inference(cnf_transformation,[],[f40]) ).

fof(f72,plain,
    ! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
    inference(cnf_transformation,[],[f44]) ).

fof(f73,plain,
    ! [X2,X0,X1] :
      ( addition(divergence(X1),forward_diamond(star(X1),domain(X2))) = addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2))))
      | addition(forward_diamond(X1,domain(X0)),domain(X2)) != addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f78,plain,
    ! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
    inference(definition_unfolding,[],[f68,f61,f61]) ).

fof(f80,plain,
    ! [X0] : divergence(X0) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))),
    inference(definition_unfolding,[],[f72,f78]) ).

fof(f81,plain,
    ! [X2,X0,X1] :
      ( addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2)))))))) = addition(antidomain(antidomain(X0)),addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2)))))))))
      | addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2))) != addition(antidomain(antidomain(X0)),addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2)))) ),
    inference(definition_unfolding,[],[f73,f78,f61,f61,f78,f61,f78,f61,f61,f61,f78,f61,f61]) ).

cnf(c_49,plain,
    addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f47]) ).

cnf(c_50,plain,
    addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_51,plain,
    addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f49]) ).

cnf(c_52,plain,
    addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f50]) ).

cnf(c_53,plain,
    multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_54,plain,
    multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f52]) ).

cnf(c_55,plain,
    multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f53]) ).

cnf(c_56,plain,
    addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_57,plain,
    addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_58,plain,
    multiplication(X0,zero) = zero,
    inference(cnf_transformation,[],[f56]) ).

cnf(c_59,plain,
    multiplication(zero,X0) = zero,
    inference(cnf_transformation,[],[f57]) ).

cnf(c_60,plain,
    multiplication(antidomain(X0),X0) = zero,
    inference(cnf_transformation,[],[f58]) ).

cnf(c_61,plain,
    addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_62,plain,
    addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
    inference(cnf_transformation,[],[f60]) ).

cnf(c_63,plain,
    multiplication(X0,coantidomain(X0)) = zero,
    inference(cnf_transformation,[],[f62]) ).

cnf(c_64,plain,
    addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_65,plain,
    addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
    inference(cnf_transformation,[],[f64]) ).

cnf(c_66,plain,
    antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))) = divergence(X0),
    inference(cnf_transformation,[],[f80]) ).

cnf(c_67,plain,
    ( addition(antidomain(antidomain(X0)),addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2)))) != addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2)))
    | addition(antidomain(antidomain(X0)),addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2))))))))) = addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2)))))))) ),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_85,plain,
    addition(antidomain(X0),antidomain(antidomain(X0))) = one,
    inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).

cnf(c_86,plain,
    addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
    inference(theory_normalisation,[status(thm)],[c_65,c_50,c_49]) ).

cnf(c_131,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_132,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_133,plain,
    ( X0 != X1
    | X2 != X3
    | addition(X0,X2) = addition(X1,X3) ),
    theory(equality) ).

cnf(c_134,plain,
    ( X0 != X1
    | X2 != X3
    | multiplication(X0,X2) = multiplication(X1,X3) ),
    theory(equality) ).

cnf(c_135,plain,
    ( X0 != X1
    | antidomain(X0) = antidomain(X1) ),
    theory(equality) ).

cnf(c_136,plain,
    ( X0 != X1
    | coantidomain(X0) = coantidomain(X1) ),
    theory(equality) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE174+1 : TPTP v8.1.2. Released v6.4.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Tue Aug 29 12:15:18 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.62  WARNING - Could not infer the problem pformat. Setting FOF as default
% 1.29/1.18  % SZS status Started for theBenchmark.p
% 1.29/1.18  % SZS status Satisfiable for theBenchmark.p
% 1.29/1.18  
% 1.29/1.18  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.29/1.18  
% 1.29/1.18  ------  iProver source info
% 1.29/1.18  
% 1.29/1.18  git: date: 2023-05-31 18:12:56 +0000
% 1.29/1.18  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.29/1.18  git: non_committed_changes: false
% 1.29/1.18  git: last_make_outside_of_git: false
% 1.29/1.18  
% 1.29/1.18  ------ Parsing...
% 1.29/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.29/1.18  
% 1.29/1.18  ------ Preprocessing... sup_sim: 0  sf_s  rm: 25 0s  sf_e  pe_s  pe_e  sf_s  rm: 6 0s  sf_e  pe_s  pe_e 
% 1.29/1.18  
% 1.29/1.18  ------ Preprocessing...------  preprocesses with Option_epr_horn
% 1.29/1.18   gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.29/1.18  ------ Proving...
% 1.29/1.18  ------ Problem Properties 
% 1.29/1.18  
% 1.29/1.18  
% 1.29/1.18  clauses                                 0
% 1.29/1.18  conjectures                             0
% 1.29/1.18  EPR                                     0
% 1.29/1.18  Horn                                    0
% 1.29/1.18  unary                                   0
% 1.29/1.18  binary                                  0
% 1.29/1.18  lits                                    0
% 1.29/1.18  lits eq                                 0
% 1.29/1.18  fd_pure                                 0
% 1.29/1.18  fd_pseudo                               0
% 1.29/1.18  fd_cond                                 0
% 1.29/1.18  fd_pseudo_cond                          0
% 1.29/1.18  AC symbols                              0
% 1.29/1.18  
% 1.29/1.18  ------ Schedule EPR Horn non eq is on
% 1.29/1.18  
% 1.29/1.18  ------ no conjectures: strip conj schedule 
% 1.29/1.18  
% 1.29/1.18  ------ no equalities: superposition off 
% 1.29/1.18  
% 1.29/1.18  ------ Option_epr_horn stripped conjectures Time Limit: Unbounded
% 1.29/1.18  
% 1.29/1.18  
% 1.29/1.18  
% 1.29/1.18  
% 1.29/1.18  % SZS status Satisfiable for theBenchmark.p
% 1.29/1.18  
% 1.29/1.18  % SZS output start Saturation for theBenchmark.p
% See solution above
% 1.29/1.18  
% 1.29/1.18  
%------------------------------------------------------------------------------