TSTP Solution File: COL006-4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : COL006-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n011.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 : Sun May  5 04:45:32 EDT 2024

% Result   : Unsatisfiable 155.93s 22.57s
% Output   : Refutation 155.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   23 (  21 unt;   0 def)
%            Number of atoms       :   25 (  21 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   10 (   8   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   44 (  44   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f105685,plain,
    $false,
    inference(subsumption_resolution,[],[f105684,f16969]) ).

fof(f16969,plain,
    ! [X0,X1] : apply(apply(apply(s,apply(apply(s,s),apply(s,k))),X1),apply(s,apply(k,X0))) = apply(X0,apply(apply(apply(s,X1),X1),apply(s,apply(k,X0)))),
    inference(forward_demodulation,[],[f16481,f1]) ).

fof(f1,axiom,
    ! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).

fof(f16481,plain,
    ! [X0,X1] : apply(apply(apply(s,apply(apply(s,s),apply(s,k))),X1),apply(s,apply(k,X0))) = apply(X0,apply(apply(X1,apply(s,apply(k,X0))),apply(X1,apply(s,apply(k,X0))))),
    inference(superposition,[],[f106,f8]) ).

fof(f8,plain,
    ! [X2,X3,X0,X1] : apply(apply(apply(s,apply(apply(s,X0),X1)),X3),X2) = apply(apply(apply(X0,X2),apply(X1,X2)),apply(X3,X2)),
    inference(superposition,[],[f1,f1]) ).

fof(f106,plain,
    ! [X2,X0,X1] : apply(X0,apply(X1,X1)) = apply(apply(apply(s,apply(s,apply(k,X0))),apply(apply(s,k),X2)),X1),
    inference(superposition,[],[f21,f7]) ).

fof(f7,plain,
    ! [X2,X0,X1] : apply(X0,apply(X2,X1)) = apply(apply(apply(s,apply(k,X0)),X2),X1),
    inference(superposition,[],[f1,f2]) ).

fof(f2,axiom,
    ! [X0,X1] : apply(apply(k,X0),X1) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).

fof(f21,plain,
    ! [X2,X0,X1] : apply(apply(apply(s,X2),apply(apply(s,k),X0)),X1) = apply(apply(X2,X1),X1),
    inference(superposition,[],[f1,f13]) ).

fof(f13,plain,
    ! [X0,X1] : apply(apply(apply(s,k),X1),X0) = X0,
    inference(superposition,[],[f1,f2]) ).

fof(f105684,plain,
    apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))) != apply(fixed_pt,apply(apply(apply(s,apply(apply(s,s),apply(s,k))),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))),
    inference(forward_demodulation,[],[f105683,f2484]) ).

fof(f2484,plain,
    ! [X2,X0,X1] : apply(apply(apply(apply(s,s),apply(apply(s,k),X0)),X1),X2) = apply(apply(apply(s,X1),X1),X2),
    inference(superposition,[],[f1208,f13]) ).

fof(f1208,plain,
    ! [X2,X0,X1] : apply(apply(apply(apply(s,s),X2),X0),X1) = apply(apply(apply(s,X0),apply(X2,X0)),X1),
    inference(superposition,[],[f6,f1]) ).

fof(f6,plain,
    ! [X2,X0,X1] : apply(apply(X0,X2),apply(apply(X1,X0),X2)) = apply(apply(apply(apply(s,s),X1),X0),X2),
    inference(superposition,[],[f1,f1]) ).

fof(f105683,plain,
    apply(apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt))) != apply(fixed_pt,apply(apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))),apply(s,apply(k,fixed_pt)))),
    inference(forward_demodulation,[],[f105682,f2]) ).

fof(f105682,plain,
    apply(apply(apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k)))),fixed_pt),apply(s,apply(k,fixed_pt))) != apply(fixed_pt,apply(apply(apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k)))),fixed_pt),apply(s,apply(k,fixed_pt)))),
    inference(forward_demodulation,[],[f105681,f2]) ).

fof(f105681,plain,
    apply(apply(apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k)))),fixed_pt),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt))) != apply(fixed_pt,apply(apply(apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k)))),fixed_pt),apply(apply(apply(k,s),fixed_pt),apply(k,fixed_pt)))),
    inference(forward_demodulation,[],[f105255,f42226]) ).

fof(f42226,plain,
    ! [X2,X3,X0,X1] : apply(apply(X0,X3),apply(apply(X1,X3),apply(X2,X3))) = apply(apply(X0,X3),apply(apply(apply(s,X1),X2),X3)),
    inference(superposition,[],[f11,f1]) ).

fof(f11,plain,
    ! [X2,X3,X0,X1] : apply(apply(apply(s,X3),apply(apply(s,X0),X1)),X2) = apply(apply(X3,X2),apply(apply(X0,X2),apply(X1,X2))),
    inference(superposition,[],[f1,f1]) ).

fof(f105255,plain,
    apply(apply(apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k)))),fixed_pt),apply(apply(apply(s,apply(k,s)),k),fixed_pt)) != apply(fixed_pt,apply(apply(apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k)))),fixed_pt),apply(apply(apply(s,apply(k,s)),k),fixed_pt))),
    inference(unit_resulting_resolution,[],[f4,f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( apply(apply(X0,fixed_pt),apply(X1,fixed_pt)) != apply(fixed_pt,apply(apply(X0,fixed_pt),apply(X1,fixed_pt)))
      | fixed_point(apply(apply(s,X0),X1)) ),
    inference(superposition,[],[f3,f1]) ).

fof(f3,axiom,
    ! [X3] :
      ( apply(X3,fixed_pt) != apply(fixed_pt,apply(X3,fixed_pt))
      | fixed_point(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).

fof(f4,axiom,
    ~ fixed_point(apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : COL006-4 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n011.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   : Fri May  3 18:32:53 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (23938)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (23941)WARNING: value z3 for option sas not known
% 0.14/0.38  % (23940)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (23939)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (23941)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (23943)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38  % (23944)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38  % (23945)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38  % (23942)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [4]
% 0.14/0.40  TRYING [5]
% 0.14/0.40  TRYING [4]
% 0.21/0.43  TRYING [5]
% 0.21/0.43  TRYING [6]
% 0.21/0.50  TRYING [7]
% 0.21/0.52  TRYING [6]
% 2.03/0.65  TRYING [8]
% 2.95/0.79  TRYING [7]
% 4.57/1.04  TRYING [9]
% 7.81/1.47  TRYING [1]
% 7.81/1.48  TRYING [2]
% 7.81/1.48  TRYING [3]
% 7.81/1.48  TRYING [4]
% 7.81/1.49  TRYING [5]
% 8.17/1.52  TRYING [6]
% 8.42/1.57  TRYING [7]
% 9.00/1.67  TRYING [8]
% 10.04/1.78  TRYING [10]
% 11.91/2.05  TRYING [9]
% 12.15/2.10  TRYING [8]
% 21.61/3.49  TRYING [11]
% 27.50/4.27  TRYING [10]
% 39.89/6.04  TRYING [11]
% 44.55/6.78  TRYING [9]
% 61.78/9.17  TRYING [12]
% 69.95/10.35  TRYING [12]
% 155.67/22.54  % (23945)First to succeed.
% 155.93/22.55  % (23945)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23938"
% 155.93/22.57  % (23945)Refutation found. Thanks to Tanya!
% 155.93/22.57  % SZS status Unsatisfiable for theBenchmark
% 155.93/22.57  % SZS output start Proof for theBenchmark
% See solution above
% 155.93/22.57  % (23945)------------------------------
% 155.93/22.57  % (23945)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 155.93/22.57  % (23945)Termination reason: Refutation
% 155.93/22.57  
% 155.93/22.57  % (23945)Memory used [KB]: 212968
% 155.93/22.57  % (23945)Time elapsed: 22.180 s
% 155.93/22.57  % (23945)Instructions burned: 68418 (million)
% 155.93/22.57  % (23938)Success in time 21.966 s
%------------------------------------------------------------------------------