TSTP Solution File: RNG008-5 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : RNG008-5 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n017.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 : Mon Jun 24 14:02:59 EDT 2024

% Result   : Unsatisfiable 4.05s 1.13s
% Output   : CNFRefutation 4.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   84 (  74 unt;   0 nHn;  32 RR)
%            Number of literals    :  114 (  83 equ;  33 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  139 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c_50,plain,
    sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).

cnf(c_52,plain,
    product(additive_identity,X0,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_id2) ).

cnf(c_53,plain,
    sum(additive_inverse(X0),additive_inverse(X1),additive_inverse(add(X0,X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute_additive_inverse) ).

cnf(c_54,plain,
    product(X0,additive_inverse(X1),additive_inverse(multiply(X0,X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_inverse) ).

cnf(c_55,plain,
    product(X0,X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_squared_is_x) ).

cnf(c_56,plain,
    product(a,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).

cnf(c_57,negated_conjecture,
    ~ product(b,a,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).

cnf(c_58,plain,
    sum(additive_identity,X0,X0),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).

cnf(c_59,plain,
    sum(X0,additive_identity,X0),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).

cnf(c_63,plain,
    sum(X0,additive_inverse(X0),additive_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).

cnf(c_65,plain,
    ( ~ sum(X0,X1,X2)
    | ~ sum(X0,X3,X4)
    | ~ sum(X1,X5,X3)
    | sum(X2,X5,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).

cnf(c_66,plain,
    ( ~ sum(X0,X1,X2)
    | sum(X1,X0,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).

cnf(c_68,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X0,X3,X4)
    | ~ product(X1,X5,X3)
    | product(X2,X5,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication2) ).

cnf(c_70,plain,
    ( ~ sum(X0,X1,X2)
    | ~ sum(X3,X4,X5)
    | ~ product(X6,X0,X3)
    | ~ product(X6,X1,X4)
    | product(X6,X2,X5) ),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity2) ).

cnf(c_72,plain,
    ( ~ sum(X0,X1,X2)
    | ~ sum(X3,X4,X5)
    | ~ product(X0,X6,X3)
    | ~ product(X1,X6,X4)
    | product(X2,X6,X5) ),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity4) ).

cnf(c_87,plain,
    add(additive_inverse(additive_inverse(X0)),additive_identity) = X0,
    inference(well_definedness,[status(thm)],[c_50]) ).

cnf(c_89,plain,
    multiply(additive_identity,X0) = additive_identity,
    inference(well_definedness,[status(thm)],[c_52]) ).

cnf(c_90,plain,
    add(additive_inverse(X0),additive_inverse(X1)) = additive_inverse(add(X0,X1)),
    inference(well_definedness,[status(thm)],[c_53]) ).

cnf(c_91,plain,
    additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
    inference(well_definedness,[status(thm)],[c_54]) ).

cnf(c_92,plain,
    multiply(X0,X0) = X0,
    inference(well_definedness,[status(thm)],[c_55]) ).

cnf(c_93,plain,
    multiply(a,b) = c,
    inference(well_definedness,[status(thm)],[c_56]) ).

cnf(c_94,plain,
    multiply(b,a) != c,
    inference(well_definedness,[status(thm)],[c_57]) ).

cnf(c_95,plain,
    add(additive_identity,X0) = X0,
    inference(well_definedness,[status(thm)],[c_58]) ).

cnf(c_96,plain,
    add(X0,additive_identity) = X0,
    inference(well_definedness,[status(thm)],[c_59]) ).

cnf(c_100,plain,
    add(X0,additive_inverse(X0)) = additive_identity,
    inference(well_definedness,[status(thm)],[c_63]) ).

cnf(c_103,plain,
    ( add(X0,X1) != X2
    | add(X0,X3) != X4
    | add(X1,X5) != X3
    | add(X2,X5) = X4 ),
    inference(well_definedness,[status(thm)],[c_65]) ).

cnf(c_105,plain,
    ( add(X0,X1) != X2
    | add(X1,X0) = X2 ),
    inference(well_definedness,[status(thm)],[c_66]) ).

cnf(c_109,plain,
    ( multiply(X0,X1) != X2
    | multiply(X0,X3) != X4
    | multiply(X1,X5) != X3
    | multiply(X2,X5) = X4 ),
    inference(well_definedness,[status(thm)],[c_68]) ).

cnf(c_113,plain,
    ( add(X0,X1) != X2
    | add(X3,X4) != X5
    | multiply(X6,X0) != X3
    | multiply(X6,X1) != X4
    | multiply(X6,X2) = X5 ),
    inference(well_definedness,[status(thm)],[c_70]) ).

cnf(c_117,plain,
    ( add(X0,X1) != X2
    | add(X3,X4) != X5
    | multiply(X0,X6) != X3
    | multiply(X1,X6) != X4
    | multiply(X2,X6) = X5 ),
    inference(well_definedness,[status(thm)],[c_72]) ).

cnf(c_249,plain,
    additive_inverse(additive_inverse(X0)) = X0,
    inference(demodulation,[status(thm)],[c_87,c_96]) ).

cnf(c_250,plain,
    add(X0,X1) = add(X1,X0),
    inference(unflattening,[status(thm)],[c_105]) ).

cnf(c_254,plain,
    multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    inference(unflattening,[status(thm)],[c_109]) ).

cnf(c_256,plain,
    add(add(X0,X1),X2) = add(X0,add(X1,X2)),
    inference(unflattening,[status(thm)],[c_103]) ).

cnf(c_258,plain,
    add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
    inference(unflattening,[status(thm)],[c_117]) ).

cnf(c_260,plain,
    add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
    inference(unflattening,[status(thm)],[c_113]) ).

cnf(c_372,plain,
    add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
    inference(superposition,[status(thm)],[c_256,c_250]) ).

cnf(c_398,plain,
    multiply(X0,additive_inverse(X0)) = additive_inverse(X0),
    inference(superposition,[status(thm)],[c_92,c_91]) ).

cnf(c_399,plain,
    multiply(a,additive_inverse(b)) = additive_inverse(c),
    inference(superposition,[status(thm)],[c_93,c_91]) ).

cnf(c_408,plain,
    multiply(X0,multiply(X0,X1)) = multiply(X0,X1),
    inference(superposition,[status(thm)],[c_92,c_254]) ).

cnf(c_409,plain,
    multiply(a,multiply(b,X0)) = multiply(c,X0),
    inference(superposition,[status(thm)],[c_93,c_254]) ).

cnf(c_412,plain,
    multiply(X0,multiply(X1,multiply(X0,X1))) = multiply(X0,X1),
    inference(superposition,[status(thm)],[c_254,c_92]) ).

cnf(c_418,plain,
    multiply(additive_inverse(X0),X0) = X0,
    inference(superposition,[status(thm)],[c_249,c_398]) ).

cnf(c_430,plain,
    multiply(add(additive_inverse(X0),additive_inverse(X1)),add(X0,X1)) = add(X0,X1),
    inference(superposition,[status(thm)],[c_90,c_418]) ).

cnf(c_434,plain,
    multiply(multiply(a,additive_inverse(b)),c) = c,
    inference(superposition,[status(thm)],[c_399,c_418]) ).

cnf(c_442,plain,
    multiply(a,multiply(additive_inverse(b),c)) = c,
    inference(demodulation,[status(thm)],[c_434,c_254]) ).

cnf(c_465,plain,
    add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
    inference(superposition,[status(thm)],[c_100,c_256]) ).

cnf(c_480,plain,
    add(multiply(X0,X1),multiply(additive_inverse(X0),X1)) = multiply(additive_identity,X1),
    inference(superposition,[status(thm)],[c_100,c_258]) ).

cnf(c_539,plain,
    multiply(a,c) = c,
    inference(superposition,[status(thm)],[c_442,c_408]) ).

cnf(c_650,plain,
    add(X0,add(additive_inverse(X0),X1)) = X1,
    inference(demodulation,[status(thm)],[c_465,c_95]) ).

cnf(c_659,plain,
    add(additive_inverse(X0),add(X0,X1)) = X1,
    inference(superposition,[status(thm)],[c_249,c_650]) ).

cnf(c_673,plain,
    add(X0,add(X1,additive_inverse(X0))) = X1,
    inference(theory_normalisation,[status(thm)],[c_659,c_256,c_250]) ).

cnf(c_982,plain,
    add(multiply(X0,X1),multiply(additive_inverse(X0),X1)) = additive_identity,
    inference(demodulation,[status(thm)],[c_480,c_89]) ).

cnf(c_986,plain,
    add(c,multiply(additive_inverse(a),b)) = additive_identity,
    inference(superposition,[status(thm)],[c_93,c_982]) ).

cnf(c_1009,plain,
    add(multiply(X0,X0),X0) = additive_identity,
    inference(superposition,[status(thm)],[c_418,c_982]) ).

cnf(c_1028,plain,
    add(X0,multiply(X0,X0)) = additive_identity,
    inference(theory_normalisation,[status(thm)],[c_1009,c_256,c_250]) ).

cnf(c_1029,plain,
    add(X0,X0) = additive_identity,
    inference(light_normalisation,[status(thm)],[c_1028,c_92]) ).

cnf(c_1075,plain,
    add(c,add(X0,multiply(additive_inverse(a),b))) = add(X0,additive_identity),
    inference(superposition,[status(thm)],[c_986,c_372]) ).

cnf(c_1078,plain,
    add(c,add(X0,multiply(additive_inverse(a),b))) = X0,
    inference(light_normalisation,[status(thm)],[c_1075,c_96]) ).

cnf(c_1096,plain,
    add(X0,additive_identity) = additive_inverse(X0),
    inference(superposition,[status(thm)],[c_1029,c_673]) ).

cnf(c_1098,plain,
    additive_inverse(X0) = X0,
    inference(light_normalisation,[status(thm)],[c_1096,c_96]) ).

cnf(c_1111,plain,
    add(X0,add(X0,X1)) = X1,
    inference(demodulation,[status(thm)],[c_650,c_1098]) ).

cnf(c_1169,plain,
    add(c,add(X0,c)) = X0,
    inference(demodulation,[status(thm)],[c_1078,c_93,c_1098]) ).

cnf(c_1178,plain,
    add(c,add(add(X0,c),X1)) = add(X0,X1),
    inference(superposition,[status(thm)],[c_1169,c_256]) ).

cnf(c_1186,plain,
    add(c,add(X0,add(c,X1))) = add(X0,X1),
    inference(theory_normalisation,[status(thm)],[c_1178,c_256,c_250]) ).

cnf(c_2309,plain,
    multiply(add(X0,additive_inverse(X1)),add(X0,X1)) = add(X0,X1),
    inference(light_normalisation,[status(thm)],[c_430,c_1098]) ).

cnf(c_2310,plain,
    add(X0,add(X1,add(multiply(X0,X1),multiply(X1,X0)))) = add(X0,X1),
    inference(demodulation,[status(thm)],[c_2309,c_92,c_250,c_256,c_258,c_260,c_372,c_1098]) ).

cnf(c_2344,plain,
    add(c,add(a,add(multiply(c,a),c))) = add(c,a),
    inference(superposition,[status(thm)],[c_539,c_2310]) ).

cnf(c_2364,plain,
    add(X0,add(multiply(X0,c),multiply(c,X0))) = add(c,add(X0,c)),
    inference(superposition,[status(thm)],[c_2310,c_1186]) ).

cnf(c_2374,plain,
    add(a,add(c,add(c,multiply(c,a)))) = add(a,c),
    inference(theory_normalisation,[status(thm)],[c_2344,c_256,c_250]) ).

cnf(c_2392,plain,
    add(X0,add(multiply(X0,c),multiply(a,multiply(b,X0)))) = X0,
    inference(light_normalisation,[status(thm)],[c_2364,c_409,c_1169]) ).

cnf(c_2679,plain,
    add(a,multiply(a,multiply(b,a))) = add(a,c),
    inference(demodulation,[status(thm)],[c_2374,c_409,c_1111]) ).

cnf(c_2681,plain,
    add(a,add(a,c)) = multiply(a,multiply(b,a)),
    inference(superposition,[status(thm)],[c_2679,c_1111]) ).

cnf(c_2696,plain,
    multiply(a,multiply(b,a)) = c,
    inference(demodulation,[status(thm)],[c_2681,c_1111]) ).

cnf(c_2702,plain,
    multiply(b,a) = multiply(b,c),
    inference(superposition,[status(thm)],[c_2696,c_412]) ).

cnf(c_2801,plain,
    add(multiply(X0,c),multiply(a,multiply(b,X0))) = add(X0,X0),
    inference(superposition,[status(thm)],[c_2392,c_1111]) ).

cnf(c_2835,plain,
    add(multiply(X0,c),multiply(a,multiply(b,X0))) = additive_identity,
    inference(light_normalisation,[status(thm)],[c_2801,c_1029]) ).

cnf(c_2919,plain,
    add(multiply(b,c),multiply(a,b)) = additive_identity,
    inference(superposition,[status(thm)],[c_92,c_2835]) ).

cnf(c_2942,plain,
    add(multiply(a,b),multiply(b,c)) = additive_identity,
    inference(theory_normalisation,[status(thm)],[c_2919,c_256,c_250]) ).

cnf(c_2943,plain,
    add(c,multiply(b,a)) = additive_identity,
    inference(light_normalisation,[status(thm)],[c_2942,c_93,c_2702]) ).

cnf(c_2970,plain,
    add(c,additive_identity) = multiply(b,a),
    inference(superposition,[status(thm)],[c_2943,c_1111]) ).

cnf(c_2984,plain,
    add(additive_identity,c) = multiply(b,a),
    inference(theory_normalisation,[status(thm)],[c_2970,c_256,c_250]) ).

cnf(c_2998,plain,
    add(additive_identity,c) != c,
    inference(demodulation,[status(thm)],[c_94,c_2984]) ).

cnf(c_2999,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_2998,c_95]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : RNG008-5 : TPTP v8.2.0. Released v1.0.0.
% 0.03/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue Jun 18 14:28:39 EDT 2024
% 0.12/0.34  % 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 --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.05/1.13  % SZS status Started for theBenchmark.p
% 4.05/1.13  % SZS status Unsatisfiable for theBenchmark.p
% 4.05/1.13  
% 4.05/1.13  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.05/1.13  
% 4.05/1.13  ------  iProver source info
% 4.05/1.13  
% 4.05/1.13  git: date: 2024-06-12 09:56:46 +0000
% 4.05/1.13  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 4.05/1.13  git: non_committed_changes: false
% 4.05/1.13  
% 4.05/1.13  ------ Parsing...successful
% 4.05/1.13  
% 4.05/1.13  
% 4.05/1.13  
% 4.05/1.13  ------ Preprocessing... sup_sim: 16  sf_s  rm: 0 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 4.05/1.13  
% 4.05/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.05/1.13  
% 4.05/1.13  ------ Preprocessing... sf_s  rm: 0 0s  sf_e 
% 4.05/1.13  ------ Proving...
% 4.05/1.13  ------ Problem Properties 
% 4.05/1.13  
% 4.05/1.13  
% 4.05/1.13  clauses                                 16
% 4.05/1.13  conjectures                             0
% 4.05/1.13  EPR                                     0
% 4.05/1.13  Horn                                    16
% 4.05/1.13  unary                                   16
% 4.05/1.13  binary                                  0
% 4.05/1.13  lits                                    16
% 4.05/1.13  lits eq                                 16
% 4.05/1.13  fd_pure                                 0
% 4.05/1.13  fd_pseudo                               0
% 4.05/1.13  fd_cond                                 0
% 4.05/1.13  fd_pseudo_cond                          0
% 4.05/1.13  AC symbols                              1
% 4.05/1.13  
% 4.05/1.13  ------ Schedule UEQ
% 4.05/1.13  
% 4.05/1.13  ------ Option_UEQ Time Limit: 10.
% 4.05/1.13  
% 4.05/1.13  
% 4.05/1.13  ------ 
% 4.05/1.13  Current options:
% 4.05/1.13  ------ 
% 4.05/1.13  
% 4.05/1.13  
% 4.05/1.13  
% 4.05/1.13  
% 4.05/1.13  ------ Proving...
% 4.05/1.13  
% 4.05/1.13  
% 4.05/1.13  % SZS status Unsatisfiable for theBenchmark.p
% 4.05/1.13  
% 4.05/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.05/1.13  
% 4.05/1.13  
%------------------------------------------------------------------------------