TSTP Solution File: GRP659+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP659+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n024.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 May 20 21:32:16 EDT 2024

% Result   : Theorem 1.41s 0.55s
% Output   : Refutation 1.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   53 (  45 unt;   0 def)
%            Number of atoms       :   63 (  62 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   25 (  15   ~;   6   |;   3   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   0 con; 1-2 aty)
%            Number of variables   :  106 ( 101   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6175,plain,
    $false,
    inference(subsumption_resolution,[],[f5066,f5115]) ).

fof(f5115,plain,
    ! [X0,X1] : mult(ld(X1,X1),X0) = X0,
    inference(forward_demodulation,[],[f5114,f14]) ).

fof(f14,plain,
    ! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).

fof(f5114,plain,
    ! [X2,X0,X1] : mult(ld(X1,X1),X0) = ld(X2,mult(X2,X0)),
    inference(forward_demodulation,[],[f5004,f17]) ).

fof(f17,plain,
    ! [X0,X1] : mult(rd(X1,X0),X0) = X1,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : mult(rd(X1,X0),X0) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).

fof(f5004,plain,
    ! [X2,X0,X1] : mult(ld(X1,X1),X0) = ld(mult(rd(X2,X0),X0),mult(X2,X0)),
    inference(superposition,[],[f60,f4861]) ).

fof(f4861,plain,
    ! [X0,X1] : mult(X1,ld(X0,X0)) = X1,
    inference(superposition,[],[f4786,f17]) ).

fof(f4786,plain,
    ! [X0,X1] : mult(X1,ld(mult(X0,X1),mult(X0,X1))) = X1,
    inference(forward_demodulation,[],[f4785,f306]) ).

fof(f306,plain,
    ! [X2,X0,X1] : mult(ld(X2,ld(X0,X1)),X2) = ld(mult(X0,X2),mult(X1,X2)),
    inference(superposition,[],[f41,f16]) ).

fof(f16,plain,
    ! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).

fof(f41,plain,
    ! [X2,X0,X1] : mult(ld(X1,X2),X1) = ld(mult(X0,X1),mult(mult(X0,X2),X1)),
    inference(superposition,[],[f14,f25]) ).

fof(f25,plain,
    ! [X2,X0,X1] : mult(mult(X2,X0),mult(ld(X0,X1),X0)) = mult(mult(X2,X1),X0),
    inference(superposition,[],[f18,f16]) ).

fof(f18,plain,
    ! [X2,X0,X1] : mult(mult(X2,mult(X1,X0)),X1) = mult(mult(X2,X1),mult(X0,X1)),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X0,X1,X2] : mult(mult(X2,mult(X1,X0)),X1) = mult(mult(X2,X1),mult(X0,X1)),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X2,X0,X1] : mult(mult(X1,mult(X0,X2)),X0) = mult(mult(X1,X0),mult(X2,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).

fof(f4785,plain,
    ! [X0,X1] : mult(X1,mult(ld(X1,ld(X0,X0)),X1)) = X1,
    inference(forward_demodulation,[],[f4681,f19]) ).

fof(f19,plain,
    ! [X0,X1] : rd(X1,ld(X0,X1)) = X0,
    inference(superposition,[],[f15,f16]) ).

fof(f15,plain,
    ! [X0,X1] : rd(mult(X1,X0),X0) = X1,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] : rd(mult(X1,X0),X0) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).

fof(f4681,plain,
    ! [X0,X1] : mult(X1,mult(ld(X1,ld(X0,X0)),X1)) = rd(ld(X0,X0),ld(X1,ld(X0,X0))),
    inference(superposition,[],[f3802,f1882]) ).

fof(f1882,plain,
    ! [X0] : ld(X0,X0) = mult(ld(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[],[f1881,f1683]) ).

fof(f1683,plain,
    ! [X0] : ld(X0,X0) = mult(X0,rd(ld(X0,X0),X0)),
    inference(superposition,[],[f14,f1616]) ).

fof(f1616,plain,
    ! [X0] : mult(X0,mult(X0,rd(ld(X0,X0),X0))) = X0,
    inference(forward_demodulation,[],[f1583,f15]) ).

fof(f1583,plain,
    ! [X0] : mult(X0,mult(X0,rd(ld(X0,X0),X0))) = rd(mult(X0,X0),X0),
    inference(superposition,[],[f69,f1562]) ).

fof(f1562,plain,
    ! [X0] : mult(X0,X0) = mult(mult(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[],[f1498,f16]) ).

fof(f1498,plain,
    ! [X0] : mult(mult(X0,X0),ld(X0,X0)) = mult(X0,mult(X0,ld(X0,X0))),
    inference(superposition,[],[f32,f225]) ).

fof(f225,plain,
    ! [X0] : ld(ld(X0,X0),X0) = X0,
    inference(superposition,[],[f14,f203]) ).

fof(f203,plain,
    ! [X1] : mult(ld(X1,X1),X1) = X1,
    inference(forward_demodulation,[],[f175,f14]) ).

fof(f175,plain,
    ! [X0,X1] : ld(X0,mult(X0,X1)) = mult(ld(X1,X1),X1),
    inference(superposition,[],[f14,f112]) ).

fof(f112,plain,
    ! [X0,X1] : mult(X0,X1) = mult(X0,mult(ld(X1,X1),X1)),
    inference(superposition,[],[f33,f17]) ).

fof(f33,plain,
    ! [X2,X0,X1] : mult(mult(rd(X0,X1),X2),X1) = mult(X0,mult(ld(X1,X2),X1)),
    inference(superposition,[],[f25,f17]) ).

fof(f32,plain,
    ! [X2,X0,X1] : mult(mult(X0,X2),ld(X0,X1)) = mult(X1,mult(ld(ld(X0,X1),X2),ld(X0,X1))),
    inference(superposition,[],[f25,f16]) ).

fof(f69,plain,
    ! [X2,X0,X1] : mult(X2,mult(X1,rd(X0,X1))) = rd(mult(mult(X2,X1),X0),X1),
    inference(superposition,[],[f30,f17]) ).

fof(f30,plain,
    ! [X2,X0,X1] : mult(X0,mult(X1,X2)) = rd(mult(mult(X0,X1),mult(X2,X1)),X1),
    inference(superposition,[],[f15,f18]) ).

fof(f1881,plain,
    ! [X0] : mult(X0,rd(ld(X0,X0),X0)) = mult(ld(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[],[f1841,f16]) ).

fof(f1841,plain,
    ! [X0] : mult(mult(X0,ld(X0,X0)),rd(ld(X0,X0),X0)) = mult(ld(X0,X0),ld(X0,X0)),
    inference(superposition,[],[f26,f1683]) ).

fof(f26,plain,
    ! [X2,X0,X1] : mult(mult(X2,rd(X0,X1)),mult(X1,rd(X0,X1))) = mult(mult(X2,X0),rd(X0,X1)),
    inference(superposition,[],[f18,f17]) ).

fof(f3802,plain,
    ! [X0,X1] : mult(X0,mult(ld(X0,X1),X0)) = rd(mult(X1,X1),ld(X0,X1)),
    inference(superposition,[],[f63,f16]) ).

fof(f63,plain,
    ! [X2,X0,X1] : mult(X0,mult(ld(X0,X1),X2)) = rd(mult(X1,mult(X2,ld(X0,X1))),ld(X0,X1)),
    inference(superposition,[],[f30,f16]) ).

fof(f60,plain,
    ! [X2,X0,X1] : mult(X2,X1) = ld(mult(rd(X0,mult(X1,X2)),X1),mult(X0,X1)),
    inference(superposition,[],[f14,f28]) ).

fof(f28,plain,
    ! [X2,X0,X1] : mult(X0,X1) = mult(mult(rd(X0,mult(X1,X2)),X1),mult(X2,X1)),
    inference(superposition,[],[f18,f17]) ).

fof(f5066,plain,
    ! [X0] : sK0(ld(X0,X0)) != mult(ld(X0,X0),sK0(ld(X0,X0))),
    inference(trivial_inequality_removal,[],[f5065]) ).

fof(f5065,plain,
    ! [X0] :
      ( sK0(ld(X0,X0)) != sK0(ld(X0,X0))
      | sK0(ld(X0,X0)) != mult(ld(X0,X0),sK0(ld(X0,X0))) ),
    inference(superposition,[],[f13,f4861]) ).

fof(f13,plain,
    ! [X0] :
      ( sK0(X0) != mult(sK0(X0),X0)
      | sK0(X0) != mult(X0,sK0(X0)) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0] :
      ( sK0(X0) != mult(X0,sK0(X0))
      | sK0(X0) != mult(sK0(X0),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f11]) ).

fof(f11,plain,
    ! [X0] :
      ( ? [X1] :
          ( mult(X0,X1) != X1
          | mult(X1,X0) != X1 )
     => ( sK0(X0) != mult(X0,sK0(X0))
        | sK0(X0) != mult(sK0(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ! [X0] :
    ? [X1] :
      ( mult(X0,X1) != X1
      | mult(X1,X0) != X1 ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,plain,
    ~ ? [X0] :
      ! [X1] :
        ( mult(X0,X1) = X1
        & mult(X1,X0) = X1 ),
    inference(rectify,[],[f7]) ).

fof(f7,negated_conjecture,
    ~ ? [X3] :
      ! [X4] :
        ( mult(X3,X4) = X4
        & mult(X4,X3) = X4 ),
    inference(negated_conjecture,[],[f6]) ).

fof(f6,conjecture,
    ? [X3] :
    ! [X4] :
      ( mult(X3,X4) = X4
      & mult(X4,X3) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12  % Problem    : GRP659+1 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 04:28:53 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (2407)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (2410)WARNING: value z3 for option sas not known
% 0.13/0.36  % (2411)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36  % (2413)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)
% 0.13/0.36  % (2414)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)
% 0.13/0.36  TRYING [1]
% 0.13/0.36  TRYING [2]
% 0.13/0.36  % (2409)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36  % (2410)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)
% 0.13/0.36  TRYING [3]
% 0.13/0.37  TRYING [4]
% 0.19/0.38  % (2408)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.38  TRYING [5]
% 0.19/0.38  TRYING [1]
% 0.19/0.38  TRYING [2]
% 0.19/0.38  % (2412)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)
% 0.19/0.39  TRYING [3]
% 0.19/0.41  TRYING [4]
% 0.19/0.41  TRYING [6]
% 0.19/0.52  TRYING [7]
% 1.41/0.55  % (2410)First to succeed.
% 1.41/0.55  % (2410)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2407"
% 1.41/0.55  % (2410)Refutation found. Thanks to Tanya!
% 1.41/0.55  % SZS status Theorem for theBenchmark
% 1.41/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 1.41/0.55  % (2410)------------------------------
% 1.41/0.55  % (2410)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.41/0.55  % (2410)Termination reason: Refutation
% 1.41/0.55  
% 1.41/0.55  % (2410)Memory used [KB]: 4201
% 1.41/0.55  % (2410)Time elapsed: 0.189 s
% 1.41/0.55  % (2410)Instructions burned: 398 (million)
% 1.41/0.55  % (2407)Success in time 0.206 s
%------------------------------------------------------------------------------