TSTP Solution File: NUM696^1 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM696^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n032.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 : Tue May 21 01:44:53 EDT 2024

% Result   : Theorem 0.17s 0.34s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   47 (  15 unt;   9 typ;   0 def)
%            Number of atoms       :   61 (  60 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  257 (  39   ~;  11   |;   1   &; 195   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :   68 (   0   ^  61   !;   7   ?;  68   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    nat: $tType ).

thf(func_def_0,type,
    nat: $tType ).

thf(func_def_1,type,
    x: nat ).

thf(func_def_2,type,
    y: nat ).

thf(func_def_3,type,
    pl: nat > nat > nat ).

thf(func_def_5,type,
    n_1: nat ).

thf(func_def_8,type,
    sK0: nat ).

thf(func_def_9,type,
    sK1: nat > nat > nat > nat ).

thf(func_def_10,type,
    sK2: nat > nat ).

thf(f83,plain,
    $false,
    inference(trivial_inequality_removal,[],[f82]) ).

thf(f82,plain,
    ( ( pl @ x @ n_1 )
   != ( pl @ x @ n_1 ) ),
    inference(superposition,[],[f37,f79]) ).

thf(f79,plain,
    n_1 = sK0,
    inference(equality_resolution,[],[f76]) ).

thf(f76,plain,
    ! [X0: nat] :
      ( ( ( pl @ x @ X0 )
       != ( pl @ x @ sK0 ) )
      | ( n_1 = X0 ) ),
    inference(superposition,[],[f72,f30]) ).

thf(f30,plain,
    ! [X0: nat,X1: nat] :
      ( ( pl @ X1 @ X0 )
      = ( pl @ X0 @ X1 ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f15,plain,
    ! [X0: nat,X1: nat] :
      ( ( pl @ X1 @ X0 )
      = ( pl @ X0 @ X1 ) ),
    inference(rectify,[],[f5]) ).

thf(f5,axiom,
    ! [X3: nat,X2: nat] :
      ( ( pl @ X2 @ X3 )
      = ( pl @ X3 @ X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).

thf(f72,plain,
    ! [X0: nat] :
      ( ( ( pl @ X0 @ x )
       != ( pl @ x @ sK0 ) )
      | ( n_1 = X0 ) ),
    inference(superposition,[],[f36,f65]) ).

thf(f65,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( pl @ X1 @ X0 )
        = ( pl @ ( pl @ X0 @ n_1 ) @ ( sK1 @ X1 @ X0 @ n_1 ) ) )
      | ( n_1 = X1 ) ),
    inference(superposition,[],[f44,f30]) ).

thf(f44,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( pl @ ( pl @ n_1 @ X1 ) @ ( sK1 @ X0 @ X1 @ n_1 ) )
        = ( pl @ X0 @ X1 ) )
      | ( n_1 = X0 ) ),
    inference(superposition,[],[f38,f32]) ).

thf(f32,plain,
    ! [X0: nat] :
      ( ( ( pl @ n_1 @ ( sK2 @ X0 ) )
        = X0 )
      | ( n_1 = X0 ) ),
    inference(cnf_transformation,[],[f28]) ).

thf(f28,plain,
    ! [X0: nat] :
      ( ( n_1 = X0 )
      | ( ( pl @ n_1 @ ( sK2 @ X0 ) )
        = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f21,f27]) ).

thf(f27,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
          ( ( pl @ n_1 @ X1 )
          = X0 )
     => ( ( pl @ n_1 @ ( sK2 @ X0 ) )
        = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f21,plain,
    ! [X0: nat] :
      ( ( n_1 = X0 )
      | ? [X1: nat] :
          ( ( pl @ n_1 @ X1 )
          = X0 ) ),
    inference(ennf_transformation,[],[f12]) ).

thf(f12,plain,
    ! [X0: nat] :
      ( ! [X1: nat] :
          ( ( pl @ n_1 @ X1 )
         != X0 )
     => ( n_1 = X0 ) ),
    inference(flattening,[],[f11]) ).

thf(f11,plain,
    ! [X0: nat] :
      ( ~ ~ ! [X1: nat] :
              ( ( pl @ n_1 @ X1 )
             != X0 )
     => ( n_1 = X0 ) ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ! [X2: nat] :
      ( ~ ~ ! [X0: nat] :
              ( ( pl @ n_1 @ X0 )
             != X2 )
     => ( n_1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz24) ).

thf(f38,plain,
    ! [X0: nat,X1: nat,X4: nat] :
      ( ( pl @ ( pl @ X0 @ X4 ) @ X1 )
      = ( pl @ ( pl @ X0 @ X1 ) @ ( sK1 @ ( pl @ X0 @ X4 ) @ X1 @ X0 ) ) ),
    inference(equality_resolution,[],[f31]) ).

thf(f31,plain,
    ! [X2: nat,X0: nat,X1: nat,X4: nat] :
      ( ( ( pl @ X2 @ X1 )
        = ( pl @ ( pl @ X0 @ X1 ) @ ( sK1 @ X2 @ X1 @ X0 ) ) )
      | ( ( pl @ X0 @ X4 )
       != X2 ) ),
    inference(cnf_transformation,[],[f26]) ).

thf(f26,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( pl @ X2 @ X1 )
        = ( pl @ ( pl @ X0 @ X1 ) @ ( sK1 @ X2 @ X1 @ X0 ) ) )
      | ! [X4: nat] :
          ( ( pl @ X0 @ X4 )
         != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f24,f25]) ).

thf(f25,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ? [X3: nat] :
          ( ( pl @ ( pl @ X0 @ X1 ) @ X3 )
          = ( pl @ X2 @ X1 ) )
     => ( ( pl @ X2 @ X1 )
        = ( pl @ ( pl @ X0 @ X1 ) @ ( sK1 @ X2 @ X1 @ X0 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f24,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ? [X3: nat] :
          ( ( pl @ ( pl @ X0 @ X1 ) @ X3 )
          = ( pl @ X2 @ X1 ) )
      | ! [X4: nat] :
          ( ( pl @ X0 @ X4 )
         != X2 ) ),
    inference(rectify,[],[f18]) ).

thf(f18,plain,
    ! [X1: nat,X2: nat,X0: nat] :
      ( ? [X4: nat] :
          ( ( pl @ X0 @ X2 )
          = ( pl @ ( pl @ X1 @ X2 ) @ X4 ) )
      | ! [X3: nat] :
          ( ( pl @ X1 @ X3 )
         != X0 ) ),
    inference(ennf_transformation,[],[f13]) ).

thf(f13,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ~ ! [X3: nat] :
            ( ( pl @ X1 @ X3 )
           != X0 )
     => ~ ! [X4: nat] :
            ( ( pl @ X0 @ X2 )
           != ( pl @ ( pl @ X1 @ X2 ) @ X4 ) ) ),
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    ! [X2: nat,X3: nat,X4: nat] :
      ( ~ ! [X0: nat] :
            ( ( pl @ X3 @ X0 )
           != X2 )
     => ~ ! [X0: nat] :
            ( ( pl @ X2 @ X4 )
           != ( pl @ ( pl @ X3 @ X4 ) @ X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).

thf(f36,plain,
    ! [X0: nat] :
      ( ( pl @ ( pl @ x @ n_1 ) @ X0 )
     != ( pl @ x @ sK0 ) ),
    inference(definition_unfolding,[],[f34,f29]) ).

thf(f29,plain,
    ( y
    = ( pl @ x @ sK0 ) ),
    inference(cnf_transformation,[],[f23]) ).

thf(f23,plain,
    ( y
    = ( pl @ x @ sK0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f19,f22]) ).

thf(f22,plain,
    ( ? [X0: nat] :
        ( y
        = ( pl @ x @ X0 ) )
   => ( y
      = ( pl @ x @ sK0 ) ) ),
    introduced(choice_axiom,[]) ).

thf(f19,plain,
    ? [X0: nat] :
      ( y
      = ( pl @ x @ X0 ) ),
    inference(ennf_transformation,[],[f1]) ).

thf(f1,axiom,
    ~ ! [X0: nat] :
        ( y
       != ( pl @ x @ X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).

thf(f34,plain,
    ! [X0: nat] :
      ( y
     != ( pl @ ( pl @ x @ n_1 ) @ X0 ) ),
    inference(cnf_transformation,[],[f17]) ).

thf(f17,plain,
    ( ! [X0: nat] :
        ( y
       != ( pl @ ( pl @ x @ n_1 ) @ X0 ) )
    & ( y
     != ( pl @ x @ n_1 ) ) ),
    inference(ennf_transformation,[],[f14]) ).

thf(f14,plain,
    ~ ( ! [X0: nat] :
          ( y
         != ( pl @ ( pl @ x @ n_1 ) @ X0 ) )
     => ( y
        = ( pl @ x @ n_1 ) ) ),
    inference(flattening,[],[f7]) ).

thf(f7,negated_conjecture,
    ~ ( ~ ~ ! [X0: nat] :
              ( y
             != ( pl @ ( pl @ x @ n_1 ) @ X0 ) )
     => ( y
        = ( pl @ x @ n_1 ) ) ),
    inference(negated_conjecture,[],[f6]) ).

thf(f6,conjecture,
    ( ~ ~ ! [X0: nat] :
            ( y
           != ( pl @ ( pl @ x @ n_1 ) @ X0 ) )
   => ( y
      = ( pl @ x @ n_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25) ).

thf(f37,plain,
    ( ( pl @ x @ n_1 )
   != ( pl @ x @ sK0 ) ),
    inference(definition_unfolding,[],[f33,f29]) ).

thf(f33,plain,
    ( y
   != ( pl @ x @ n_1 ) ),
    inference(cnf_transformation,[],[f17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem    : NUM696^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.11  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Mon May 20 06:16:37 EDT 2024
% 0.11/0.31  % CPUTime    : 
% 0.11/0.31  This is a TH0_THM_EQU_NAR problem
% 0.11/0.31  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.32  % (21031)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.17/0.32  % (21031)Instruction limit reached!
% 0.17/0.32  % (21031)------------------------------
% 0.17/0.32  % (21031)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.32  % (21031)Termination reason: Unknown
% 0.17/0.32  % (21031)Termination phase: Saturation
% 0.17/0.32  
% 0.17/0.32  % (21031)Memory used [KB]: 5373
% 0.17/0.32  % (21031)Time elapsed: 0.002 s
% 0.17/0.32  % (21031)Instructions burned: 2 (million)
% 0.17/0.32  % (21031)------------------------------
% 0.17/0.32  % (21031)------------------------------
% 0.17/0.32  % (21029)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (3000ds/4Mi)
% 0.17/0.32  % (21032)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.17/0.32  % (21033)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (3000ds/275Mi)
% 0.17/0.32  % (21029)Instruction limit reached!
% 0.17/0.32  % (21029)------------------------------
% 0.17/0.32  % (21029)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.32  % (21029)Termination reason: Unknown
% 0.17/0.32  % (21029)Termination phase: Saturation
% 0.17/0.32  
% 0.17/0.32  % (21029)Memory used [KB]: 5500
% 0.17/0.32  % (21029)Time elapsed: 0.003 s
% 0.17/0.32  % (21029)Instructions burned: 4 (million)
% 0.17/0.32  % (21029)------------------------------
% 0.17/0.32  % (21029)------------------------------
% 0.17/0.32  % (21032)Instruction limit reached!
% 0.17/0.32  % (21032)------------------------------
% 0.17/0.32  % (21032)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.32  % (21032)Termination reason: Unknown
% 0.17/0.32  % (21032)Termination phase: Property scanning
% 0.17/0.32  
% 0.17/0.32  % (21032)Memory used [KB]: 895
% 0.17/0.32  % (21032)Time elapsed: 0.002 s
% 0.17/0.32  % (21032)Instructions burned: 2 (million)
% 0.17/0.32  % (21032)------------------------------
% 0.17/0.32  % (21032)------------------------------
% 0.17/0.33  % (21034)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.17/0.33  % (21028)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.17/0.33  % (21030)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (3000ds/27Mi)
% 0.17/0.33  % (21033)Refutation not found, incomplete strategy
% 0.17/0.33  % (21033)------------------------------
% 0.17/0.33  % (21033)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.33  % (21033)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.33  
% 0.17/0.33  
% 0.17/0.33  % (21033)Memory used [KB]: 5500
% 0.17/0.33  % (21033)Time elapsed: 0.004 s
% 0.17/0.33  % (21033)Instructions burned: 5 (million)
% 0.17/0.33  % (21033)------------------------------
% 0.17/0.33  % (21033)------------------------------
% 0.17/0.33  % (21035)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.17/0.33  % (21035)Instruction limit reached!
% 0.17/0.33  % (21035)------------------------------
% 0.17/0.33  % (21035)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.33  % (21035)Termination reason: Unknown
% 0.17/0.33  % (21035)Termination phase: Saturation
% 0.17/0.33  
% 0.17/0.33  % (21035)Memory used [KB]: 5500
% 0.17/0.33  % (21035)Time elapsed: 0.002 s
% 0.17/0.33  % (21035)Instructions burned: 3 (million)
% 0.17/0.33  % (21035)------------------------------
% 0.17/0.33  % (21035)------------------------------
% 0.17/0.33  % (21037)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.17/0.33  % (21028)First to succeed.
% 0.17/0.33  % (21034)Instruction limit reached!
% 0.17/0.33  % (21034)------------------------------
% 0.17/0.33  % (21034)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.33  % (21034)Termination reason: Unknown
% 0.17/0.33  % (21034)Termination phase: Saturation
% 0.17/0.33  
% 0.17/0.33  % (21034)Memory used [KB]: 5500
% 0.17/0.33  % (21034)Time elapsed: 0.011 s
% 0.17/0.33  % (21034)Instructions burned: 18 (million)
% 0.17/0.34  % (21034)------------------------------
% 0.17/0.34  % (21034)------------------------------
% 0.17/0.34  % (21038)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.17/0.34  % (21028)Refutation found. Thanks to Tanya!
% 0.17/0.34  % SZS status Theorem for theBenchmark
% 0.17/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.34  % (21028)------------------------------
% 0.17/0.34  % (21028)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.34  % (21028)Termination reason: Refutation
% 0.17/0.34  
% 0.17/0.34  % (21028)Memory used [KB]: 5628
% 0.17/0.34  % (21028)Time elapsed: 0.012 s
% 0.17/0.34  % (21028)Instructions burned: 16 (million)
% 0.17/0.34  % (21028)------------------------------
% 0.17/0.34  % (21028)------------------------------
% 0.17/0.34  % (21027)Success in time 0.031 s
% 0.17/0.34  % Vampire---4.8 exiting
%------------------------------------------------------------------------------