TSTP Solution File: SWW486_5 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SWW486_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n023.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 18:25:28 EDT 2024

% Result   : Theorem 90.01s 13.55s
% Output   : Refutation 90.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   19 (  12 unt;   0 typ;   0 def)
%            Number of atoms       :   29 (  11 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  496 (  15   ~;   6   |;   0   &; 473   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   7 con; 0-4 aty)
%            Number of variables   :   19 (   0   ^  19   !;   0   ?;  19   :)

% Comments : 
%------------------------------------------------------------------------------
thf(complex_type,type,
    complex: $tType ).

thf(bool_type,type,
    bool: $tType ).

thf(real_type,type,
    real: $tType ).

thf(comm_semiring_0_type,type,
    comm_semiring_0: 
      !>[TA: $tType] : $o ).

thf(plus_plus_type,type,
    plus_plus: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(times_times_type,type,
    times_times: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(ord_less_eq_type,type,
    ord_less_eq: 
      !>[TA: $tType] : ( TA > TA > $o ) ).

thf(pCons_type,type,
    pCons: 
      !>[TA: $tType] : ( TA > ( poly1 @ TA ) > ( poly1 @ TA ) ) ).

thf(poly_type,type,
    poly: 
      !>[TA: $tType] : ( ( poly1 @ TA ) > ( fun @ TA @ TA ) ) ).

thf(norm_norm_type,type,
    norm_norm: 
      !>[TA: $tType] : ( TA > real ) ).

thf(aa_type,type,
    aa: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).

thf(c_type,type,
    c: complex ).

thf(cs_type,type,
    cs: poly1 @ complex ).

thf(z_type,type,
    z: complex ).

thf(53,axiom,
    ! [TA: $tType] :
      ( ( comm_semiring_0 @ TA )
     => ! [A: TA,B: poly1 @ TA,C: TA] :
          ( ( aa @ TA @ TA @ ( poly @ TA @ ( pCons @ TA @ C @ B ) ) @ A )
          = ( plus_plus @ TA @ C @ ( times_times @ TA @ A @ ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_poly__pCons) ).

thf(298,plain,
    ! [TA: $tType] :
      ( ( comm_semiring_0 @ TA )
     => ! [A: TA,B: poly1 @ TA,C: TA] :
          ( ( aa @ TA @ TA @ ( poly @ TA @ ( pCons @ TA @ C @ B ) ) @ A )
          = ( plus_plus @ TA @ C @ ( times_times @ TA @ A @ ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(299,plain,
    ! [TA: $tType,C: TA,B: poly1 @ TA,A: TA] :
      ( ~ ( comm_semiring_0 @ TA )
      | ( ( aa @ TA @ TA @ ( poly @ TA @ ( pCons @ TA @ C @ B ) ) @ A )
        = ( plus_plus @ TA @ C @ ( times_times @ TA @ A @ ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A ) ) ) ) ),
    inference(cnf,[status(esa)],[298]) ).

thf(300,plain,
    ! [TA: $tType,C: TA,B: poly1 @ TA,A: TA] :
      ( ( ( aa @ TA @ TA @ ( poly @ TA @ ( pCons @ TA @ C @ B ) ) @ A )
        = ( plus_plus @ TA @ C @ ( times_times @ TA @ A @ ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A ) ) ) )
      | ~ ( comm_semiring_0 @ TA ) ),
    inference(lifteq,[status(thm)],[299]) ).

thf(48,axiom,
    ord_less_eq @ real @ ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096cmod_A_Ic_A_L_Az_A_K_Apoly_Acs_Az_J_A_060_061_Acmod_Ac_A_L_Acmod_A_Iz_A_K_Apoly_Acs_Az_J_096) ).

thf(285,plain,
    ord_less_eq @ real @ ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(1,conjecture,
    ord_less_eq @ real @ ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( ord_less_eq @ real @ ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(187,plain,
    ~ ( ord_less_eq @ real @ ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4661,plain,
    ( ( ord_less_eq @ real @ ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) )
   != ( ord_less_eq @ real @ ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[285,187]) ).

thf(4746,plain,
    ( ( ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) )
     != ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) )
    | ( ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) )
     != ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) ) ),
    inference(simp,[status(thm)],[4661]) ).

thf(4753,plain,
    ( ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) )
   != ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) ),
    inference(simp,[status(thm)],[4746]) ).

thf(9630,plain,
    ! [C: complex,B: poly1 @ complex,A: complex] :
      ( ~ ( comm_semiring_0 @ complex )
      | ( ( norm_norm @ complex @ ( plus_plus @ complex @ C @ ( times_times @ complex @ A @ ( aa @ complex @ complex @ ( poly @ complex @ B ) @ A ) ) ) )
       != ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) )
      | ( ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ C @ B ) ) @ A )
       != ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) ) ),
    inference(paramod_ordered,[status(thm)],[300,4753]) ).

thf(9631,plain,
    ( ~ ( comm_semiring_0 @ complex )
    | ( ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) )
     != ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[9630:[bind(A,$thf( z )),bind(B,$thf( cs )),bind(C,$thf( c ))]]) ).

thf(9723,plain,
    ~ ( comm_semiring_0 @ complex ),
    inference(simp,[status(thm)],[9631]) ).

thf(182,axiom,
    comm_semiring_0 @ complex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__0) ).

thf(618,plain,
    comm_semiring_0 @ complex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(9851,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[9723,618]) ).

thf(9852,plain,
    $false,
    inference(simp,[status(thm)],[9851]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SWW486_5 : TPTP v8.2.0. Released v6.0.0.
% 0.03/0.13  % Command  : run_Leo-III %s %d SAT
% 0.12/0.34  % Computer : n023.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 : Wed Jun 19 06:14:10 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.82/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.38/0.99  % [INFO] 	 Parsing done (162ms). 
% 1.38/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.88/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.88/1.22  % [INFO] 	 Scanning for conjecture ... 
% 2.16/1.31  % [INFO] 	 Found a conjecture (or negated_conjecture) and 186 axioms. Running axiom selection ... 
% 2.44/1.38  % [INFO] 	 Axiom selection finished. Selected 184 axioms (removed 2 axioms). 
% 2.77/1.50  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 2.77/1.51  % [INFO] 	 Type checking passed. 
% 2.77/1.52  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 90.01/13.55  % [INFO] 	 Killing All external provers ... 
% 90.01/13.55  % Time passed: 13042ms (effective reasoning time: 12544ms)
% 90.01/13.55  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 90.01/13.55  % Axioms used in derivation (3): fact_4_poly__pCons, fact_0__096cmod_A_Ic_A_L_Az_A_K_Apoly_Acs_Az_J_A_060_061_Acmod_Ac_A_L_Acmod_A_Iz_A_K_Apoly_Acs_Az_J_096, arity_Complex_Ocomplex___Rings_Ocomm__semiring__0
% 90.01/13.55  % No. of inferences in proof: 19
% 90.01/13.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 13042 ms resp. 12544 ms w/o parsing
% 90.01/13.59  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 90.01/13.59  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------