TSTP Solution File: GRP682+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP682+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n021.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 Apr 30 12:08:36 EDT 2024

% Result   : Theorem 2.78s 0.82s
% Output   : Refutation 2.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :    9
% Syntax   : Number of formulae    :  101 (  90 unt;   0 def)
%            Number of atoms       :  114 ( 113 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   35 (  22   ~;   9   |;   3   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  216 ( 210   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f19134,plain,
    $false,
    inference(trivial_inequality_removal,[],[f19056]) ).

fof(f19056,plain,
    mult(sK0,ld(sK0,sK2)) != mult(sK0,ld(sK0,sK2)),
    inference(superposition,[],[f3379,f10679]) ).

fof(f10679,plain,
    ! [X2,X0,X1] : mult(X0,ld(X0,X2)) = mult(rd(X0,X1),ld(rd(X0,X1),X2)),
    inference(forward_demodulation,[],[f10678,f6579]) ).

fof(f6579,plain,
    ! [X2,X0,X1] : mult(X0,ld(X0,X2)) = mult(mult(X0,X1),ld(mult(X0,X1),X2)),
    inference(forward_demodulation,[],[f6488,f1442]) ).

fof(f1442,plain,
    ! [X0,X1] : mult(X0,ld(X0,X1)) = mult(ld(X0,X0),ld(ld(X0,X0),X1)),
    inference(forward_demodulation,[],[f1398,f1041]) ).

fof(f1041,plain,
    ! [X0,X1] : mult(X0,ld(X0,X1)) = mult(ld(X0,X0),X1),
    inference(forward_demodulation,[],[f996,f57]) ).

fof(f57,plain,
    ! [X0] : mult(ld(X0,X0),X0) = X0,
    inference(superposition,[],[f35,f49]) ).

fof(f49,plain,
    ! [X0] : rd(X0,X0) = ld(X0,X0),
    inference(forward_demodulation,[],[f43,f33]) ).

fof(f33,plain,
    ! [X0] : ld(X0,X0) = mult(X0,ld(X0,ld(X0,X0))),
    inference(superposition,[],[f22,f31]) ).

fof(f31,plain,
    ! [X0] : mult(X0,ld(X0,X0)) = X0,
    inference(superposition,[],[f22,f21]) ).

fof(f21,plain,
    ! [X0] : ld(X0,mult(X0,X0)) = X0,
    inference(cnf_transformation,[],[f1]) ).

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

fof(f22,plain,
    ! [X0,X1] : mult(X1,ld(X1,X0)) = ld(X1,mult(X1,X0)),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1] : mult(X1,ld(X1,X0)) = ld(X1,mult(X1,X0)),
    inference(rectify,[],[f3]) ).

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

fof(f43,plain,
    ! [X0] : rd(X0,X0) = mult(X0,ld(X0,ld(X0,X0))),
    inference(superposition,[],[f28,f37]) ).

fof(f37,plain,
    ! [X0] : rd(X0,X0) = mult(rd(rd(X0,X0),X0),X0),
    inference(superposition,[],[f23,f35]) ).

fof(f23,plain,
    ! [X0,X1] : mult(rd(X1,X0),X0) = rd(mult(X1,X0),X0),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] : mult(rd(X1,X0),X0) = rd(mult(X1,X0),X0),
    inference(rectify,[],[f4]) ).

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

fof(f28,plain,
    ! [X0,X1] : mult(rd(rd(X1,X1),X0),X0) = mult(X1,ld(X1,ld(X0,X0))),
    inference(forward_demodulation,[],[f27,f22]) ).

fof(f27,plain,
    ! [X0,X1] : ld(X1,mult(X1,ld(X0,X0))) = mult(rd(rd(X1,X1),X0),X0),
    inference(forward_demodulation,[],[f24,f23]) ).

fof(f24,plain,
    ! [X0,X1] : ld(X1,mult(X1,ld(X0,X0))) = rd(mult(rd(X1,X1),X0),X0),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] : ld(X1,mult(X1,ld(X0,X0))) = rd(mult(rd(X1,X1),X0),X0),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).

fof(f35,plain,
    ! [X0] : mult(rd(X0,X0),X0) = X0,
    inference(superposition,[],[f23,f20]) ).

fof(f20,plain,
    ! [X0] : rd(mult(X0,X0),X0) = X0,
    inference(cnf_transformation,[],[f2]) ).

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

fof(f996,plain,
    ! [X0,X1] : mult(ld(X0,X0),X1) = mult(X0,ld(X0,mult(ld(X1,X1),X1))),
    inference(superposition,[],[f929,f303]) ).

fof(f303,plain,
    ! [X0,X1] : mult(ld(X0,X0),X1) = mult(mult(X0,ld(X0,ld(X1,X1))),X1),
    inference(forward_demodulation,[],[f290,f49]) ).

fof(f290,plain,
    ! [X0,X1] : mult(rd(X0,X0),X1) = mult(mult(X0,ld(X0,ld(X1,X1))),X1),
    inference(superposition,[],[f278,f28]) ).

fof(f278,plain,
    ! [X0,X1] : mult(X0,X1) = mult(mult(rd(X0,X1),X1),X1),
    inference(forward_demodulation,[],[f247,f35]) ).

fof(f247,plain,
    ! [X0,X1] : mult(X0,mult(rd(X1,X1),X1)) = mult(mult(rd(X0,X1),X1),X1),
    inference(superposition,[],[f153,f23]) ).

fof(f153,plain,
    ! [X2,X0,X1] : mult(X0,mult(rd(X1,X2),X2)) = mult(rd(mult(X0,X1),X2),X2),
    inference(superposition,[],[f117,f23]) ).

fof(f117,plain,
    ! [X2,X0,X1] : mult(X1,mult(rd(X2,X0),X0)) = rd(mult(mult(X1,X2),X0),X0),
    inference(superposition,[],[f29,f20]) ).

fof(f29,plain,
    ! [X2,X3,X0,X1] : rd(mult(mult(X3,X2),rd(X1,X0)),rd(X1,X0)) = mult(X3,mult(rd(X2,X0),X0)),
    inference(forward_demodulation,[],[f25,f23]) ).

fof(f25,plain,
    ! [X2,X3,X0,X1] : rd(mult(mult(X3,X2),rd(X1,X0)),rd(X1,X0)) = mult(X3,rd(mult(X2,X0),X0)),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1,X2,X3] : rd(mult(mult(X3,X2),rd(X1,X0)),rd(X1,X0)) = mult(X3,rd(mult(X2,X0),X0)),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2,X3,X1,X0] : rd(mult(mult(X0,X1),rd(X3,X2)),rd(X3,X2)) = mult(X0,rd(mult(X1,X2),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).

fof(f929,plain,
    ! [X2,X0,X1] : mult(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,X2))),
    inference(forward_demodulation,[],[f891,f22]) ).

fof(f891,plain,
    ! [X2,X0,X1] : mult(mult(X0,ld(X0,X1)),X2) = ld(X0,mult(X0,mult(X1,X2))),
    inference(superposition,[],[f30,f21]) ).

fof(f30,plain,
    ! [X2,X3,X0,X1] : ld(ld(X3,X2),mult(ld(X3,X2),mult(X1,X0))) = mult(mult(X3,ld(X3,X1)),X0),
    inference(forward_demodulation,[],[f26,f22]) ).

fof(f26,plain,
    ! [X2,X3,X0,X1] : ld(ld(X3,X2),mult(ld(X3,X2),mult(X1,X0))) = mult(ld(X3,mult(X3,X1)),X0),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1,X2,X3] : ld(ld(X3,X2),mult(ld(X3,X2),mult(X1,X0))) = mult(ld(X3,mult(X3,X1)),X0),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X2,X3,X1,X0] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X3,X2))) = mult(ld(X0,mult(X0,X3)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).

fof(f1398,plain,
    ! [X0,X1] : mult(ld(X0,X0),X1) = mult(ld(X0,X0),ld(ld(X0,X0),X1)),
    inference(superposition,[],[f1041,f384]) ).

fof(f384,plain,
    ! [X0] : ld(X0,X0) = ld(ld(X0,X0),ld(X0,X0)),
    inference(superposition,[],[f21,f368]) ).

fof(f368,plain,
    ! [X0] : ld(X0,X0) = mult(ld(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[],[f367,f33]) ).

fof(f367,plain,
    ! [X0] : mult(X0,ld(X0,ld(X0,X0))) = mult(ld(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[],[f355,f55]) ).

fof(f55,plain,
    ! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(rd(ld(X0,X0),X1),X1),
    inference(superposition,[],[f28,f49]) ).

fof(f355,plain,
    ! [X0] : mult(rd(ld(X0,X0),X0),X0) = mult(ld(X0,X0),ld(X0,X0)),
    inference(superposition,[],[f159,f31]) ).

fof(f159,plain,
    ! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,mult(X0,ld(X0,ld(X1,X1)))),
    inference(forward_demodulation,[],[f158,f23]) ).

fof(f158,plain,
    ! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,mult(X0,ld(X0,ld(X1,X1)))),
    inference(forward_demodulation,[],[f132,f55]) ).

fof(f132,plain,
    ! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,mult(rd(ld(X0,X0),X1),X1)),
    inference(superposition,[],[f117,f31]) ).

fof(f6488,plain,
    ! [X2,X0,X1] : mult(mult(X0,X1),ld(mult(X0,X1),X2)) = mult(ld(X0,X0),ld(ld(X0,X0),X2)),
    inference(superposition,[],[f3676,f4892]) ).

fof(f4892,plain,
    ! [X0,X1] : mult(X0,X1) = ld(ld(X0,X0),mult(X0,X1)),
    inference(superposition,[],[f949,f4788]) ).

fof(f4788,plain,
    ! [X0,X1] : mult(X0,X1) = mult(ld(X0,X0),mult(X0,X1)),
    inference(forward_demodulation,[],[f4737,f1030]) ).

fof(f1030,plain,
    ! [X0,X1] : mult(X0,X1) = mult(X0,mult(X0,ld(X0,X1))),
    inference(forward_demodulation,[],[f989,f22]) ).

fof(f989,plain,
    ! [X0,X1] : mult(X0,X1) = mult(X0,ld(X0,mult(X0,X1))),
    inference(superposition,[],[f929,f31]) ).

fof(f4737,plain,
    ! [X0,X1] : mult(X0,mult(X0,ld(X0,X1))) = mult(ld(X0,X0),mult(X0,mult(X0,ld(X0,X1)))),
    inference(superposition,[],[f3422,f22]) ).

fof(f3422,plain,
    ! [X0,X1] : mult(X0,ld(X0,X1)) = mult(ld(X0,X0),mult(X0,ld(X0,X1))),
    inference(forward_demodulation,[],[f3421,f1041]) ).

fof(f3421,plain,
    ! [X0,X1] : mult(ld(X0,X0),X1) = mult(ld(X0,X0),mult(ld(X0,X0),X1)),
    inference(forward_demodulation,[],[f3380,f368]) ).

fof(f3380,plain,
    ! [X0,X1] : mult(mult(ld(X0,X0),ld(X0,X0)),X1) = mult(ld(X0,X0),mult(mult(ld(X0,X0),ld(X0,X0)),X1)),
    inference(superposition,[],[f2001,f384]) ).

fof(f2001,plain,
    ! [X0,X1] : mult(mult(X0,X0),X1) = mult(ld(X0,X0),mult(mult(X0,X0),X1)),
    inference(forward_demodulation,[],[f1965,f31]) ).

fof(f1965,plain,
    ! [X0,X1] : mult(ld(X0,X0),mult(mult(X0,X0),X1)) = mult(mult(mult(X0,X0),X1),ld(mult(mult(X0,X0),X1),mult(mult(X0,X0),X1))),
    inference(superposition,[],[f972,f985]) ).

fof(f985,plain,
    ! [X0,X1] : mult(mult(X0,X0),X1) = mult(X0,ld(X0,mult(mult(X0,X0),X1))),
    inference(superposition,[],[f929,f21]) ).

fof(f972,plain,
    ! [X0,X1] : mult(mult(X1,ld(X1,X0)),ld(X0,X0)) = mult(ld(X1,X1),X0),
    inference(forward_demodulation,[],[f971,f312]) ).

fof(f312,plain,
    ! [X0] : rd(X0,ld(X0,X0)) = X0,
    inference(superposition,[],[f304,f34]) ).

fof(f34,plain,
    ! [X0] : rd(X0,ld(X0,X0)) = mult(rd(X0,ld(X0,X0)),ld(X0,X0)),
    inference(superposition,[],[f23,f31]) ).

fof(f304,plain,
    ! [X0] : mult(rd(X0,ld(X0,X0)),ld(X0,X0)) = X0,
    inference(forward_demodulation,[],[f293,f31]) ).

fof(f293,plain,
    ! [X0] : mult(X0,ld(X0,X0)) = mult(rd(X0,ld(X0,X0)),ld(X0,X0)),
    inference(superposition,[],[f278,f34]) ).

fof(f971,plain,
    ! [X0,X1] : mult(mult(X1,ld(X1,rd(X0,ld(X0,X0)))),ld(X0,X0)) = mult(ld(X1,X1),rd(X0,ld(X0,X0))),
    inference(forward_demodulation,[],[f919,f949]) ).

fof(f919,plain,
    ! [X2,X0,X1] : mult(mult(X1,ld(X1,rd(X0,ld(X0,X0)))),ld(X0,X0)) = ld(ld(X1,X2),mult(ld(X1,X2),rd(X0,ld(X0,X0)))),
    inference(superposition,[],[f30,f34]) ).

fof(f949,plain,
    ! [X2,X0,X1] : ld(ld(X1,X2),mult(ld(X1,X2),X0)) = mult(ld(X1,X1),X0),
    inference(forward_demodulation,[],[f905,f303]) ).

fof(f905,plain,
    ! [X2,X0,X1] : ld(ld(X1,X2),mult(ld(X1,X2),X0)) = mult(mult(X1,ld(X1,ld(X0,X0))),X0),
    inference(superposition,[],[f30,f57]) ).

fof(f3676,plain,
    ! [X2,X0,X1] : mult(X0,ld(X0,X2)) = mult(ld(X0,X1),ld(ld(X0,X1),X2)),
    inference(forward_demodulation,[],[f3641,f1041]) ).

fof(f3641,plain,
    ! [X2,X0,X1] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(ld(X0,X0),X2),
    inference(superposition,[],[f949,f22]) ).

fof(f10678,plain,
    ! [X2,X0,X1] : mult(mult(X0,X1),ld(mult(X0,X1),X2)) = mult(rd(X0,X1),ld(rd(X0,X1),X2)),
    inference(forward_demodulation,[],[f10677,f22]) ).

fof(f10677,plain,
    ! [X2,X0,X1] : ld(mult(X0,X1),mult(mult(X0,X1),X2)) = mult(rd(X0,X1),ld(rd(X0,X1),X2)),
    inference(forward_demodulation,[],[f10540,f6579]) ).

fof(f10540,plain,
    ! [X2,X0,X1] : ld(mult(X0,X1),mult(mult(X0,X1),X2)) = mult(mult(rd(X0,X1),X1),ld(mult(rd(X0,X1),X1),X2)),
    inference(superposition,[],[f5076,f278]) ).

fof(f5076,plain,
    ! [X2,X0,X1] : mult(X0,ld(X0,X2)) = ld(mult(X0,X1),mult(mult(X0,X1),X2)),
    inference(forward_demodulation,[],[f5035,f3655]) ).

fof(f3655,plain,
    ! [X0,X1,X4] : mult(ld(ld(X0,X1),ld(X0,X1)),X4) = mult(X0,ld(X0,X4)),
    inference(forward_demodulation,[],[f3654,f3652]) ).

fof(f3652,plain,
    ! [X2,X0,X1] : mult(X0,ld(X0,X2)) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))),
    inference(forward_demodulation,[],[f3651,f1041]) ).

fof(f3651,plain,
    ! [X2,X0,X1] : mult(ld(X0,X0),X2) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))),
    inference(forward_demodulation,[],[f3612,f929]) ).

fof(f3612,plain,
    ! [X2,X0,X1] : mult(ld(X0,X0),X2) = ld(mult(X0,ld(X0,X1)),mult(mult(X0,ld(X0,X1)),X2)),
    inference(superposition,[],[f949,f22]) ).

fof(f3654,plain,
    ! [X2,X3,X0,X1,X4] : mult(ld(ld(X0,X1),ld(X0,X1)),X4) = ld(mult(X0,ld(X0,mult(X2,X3))),mult(X0,ld(X0,mult(mult(X2,X3),X4)))),
    inference(forward_demodulation,[],[f3653,f929]) ).

fof(f3653,plain,
    ! [X2,X3,X0,X1,X4] : mult(ld(ld(X0,X1),ld(X0,X1)),X4) = ld(mult(X0,ld(X0,mult(X2,X3))),mult(mult(X0,ld(X0,mult(X2,X3))),X4)),
    inference(forward_demodulation,[],[f3613,f929]) ).

fof(f3613,plain,
    ! [X2,X3,X0,X1,X4] : mult(ld(ld(X0,X1),ld(X0,X1)),X4) = ld(mult(mult(X0,ld(X0,X2)),X3),mult(mult(mult(X0,ld(X0,X2)),X3),X4)),
    inference(superposition,[],[f949,f30]) ).

fof(f5035,plain,
    ! [X2,X0,X1] : ld(mult(X0,X1),mult(mult(X0,X1),X2)) = mult(ld(ld(X0,X0),ld(X0,X0)),X2),
    inference(superposition,[],[f949,f4892]) ).

fof(f3379,plain,
    mult(rd(sK0,sK1),ld(rd(sK0,sK1),sK2)) != mult(sK0,ld(sK0,sK2)),
    inference(subsumption_resolution,[],[f3378,f22]) ).

fof(f3378,plain,
    ( ld(sK0,mult(sK0,sK2)) != mult(sK0,ld(sK0,sK2))
    | mult(rd(sK0,sK1),ld(rd(sK0,sK1),sK2)) != mult(sK0,ld(sK0,sK2)) ),
    inference(forward_demodulation,[],[f3377,f1041]) ).

fof(f3377,plain,
    ( ld(sK0,mult(sK0,sK2)) != mult(ld(sK0,sK0),sK2)
    | mult(rd(sK0,sK1),ld(rd(sK0,sK1),sK2)) != mult(sK0,ld(sK0,sK2)) ),
    inference(forward_demodulation,[],[f3376,f949]) ).

fof(f3376,plain,
    ( mult(rd(sK0,sK1),ld(rd(sK0,sK1),sK2)) != mult(sK0,ld(sK0,sK2))
    | ld(sK0,mult(sK0,sK2)) != ld(ld(sK0,sK1),mult(ld(sK0,sK1),sK2)) ),
    inference(forward_demodulation,[],[f3375,f22]) ).

fof(f3375,plain,
    ( ld(sK0,mult(sK0,sK2)) != mult(rd(sK0,sK1),ld(rd(sK0,sK1),sK2))
    | ld(sK0,mult(sK0,sK2)) != ld(ld(sK0,sK1),mult(ld(sK0,sK1),sK2)) ),
    inference(superposition,[],[f19,f22]) ).

fof(f19,plain,
    ( ld(sK0,mult(sK0,sK2)) != ld(rd(sK0,sK1),mult(rd(sK0,sK1),sK2))
    | ld(sK0,mult(sK0,sK2)) != ld(ld(sK0,sK1),mult(ld(sK0,sK1),sK2)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( ld(sK0,mult(sK0,sK2)) != ld(rd(sK0,sK1),mult(rd(sK0,sK1),sK2))
    | ld(sK0,mult(sK0,sK2)) != ld(ld(sK0,sK1),mult(ld(sK0,sK1),sK2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f17]) ).

fof(f17,plain,
    ( ? [X0,X1,X2] :
        ( ld(X0,mult(X0,X2)) != ld(rd(X0,X1),mult(rd(X0,X1),X2))
        | ld(X0,mult(X0,X2)) != ld(ld(X0,X1),mult(ld(X0,X1),X2)) )
   => ( ld(sK0,mult(sK0,sK2)) != ld(rd(sK0,sK1),mult(rd(sK0,sK1),sK2))
      | ld(sK0,mult(sK0,sK2)) != ld(ld(sK0,sK1),mult(ld(sK0,sK1),sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0,X1,X2] :
      ( ld(X0,mult(X0,X2)) != ld(rd(X0,X1),mult(rd(X0,X1),X2))
      | ld(X0,mult(X0,X2)) != ld(ld(X0,X1),mult(ld(X0,X1),X2)) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,plain,
    ~ ! [X0,X1,X2] :
        ( ld(X0,mult(X0,X2)) = ld(rd(X0,X1),mult(rd(X0,X1),X2))
        & ld(X0,mult(X0,X2)) = ld(ld(X0,X1),mult(ld(X0,X1),X2)) ),
    inference(rectify,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X4,X5,X6] :
        ( ld(X4,mult(X4,X6)) = ld(rd(X4,X5),mult(rd(X4,X5),X6))
        & ld(ld(X4,X5),mult(ld(X4,X5),X6)) = ld(X4,mult(X4,X6)) ),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X4,X5,X6] :
      ( ld(X4,mult(X4,X6)) = ld(rd(X4,X5),mult(rd(X4,X5),X6))
      & ld(ld(X4,X5),mult(ld(X4,X5),X6)) = ld(X4,mult(X4,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : GRP682+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.37  % Computer : n021.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 300
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Tue Apr 30 04:35:40 EDT 2024
% 0.14/0.37  % CPUTime    : 
% 0.14/0.37  % (16045)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39  % (16048)WARNING: value z3 for option sas not known
% 0.14/0.39  % (16050)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)
% 0.14/0.39  % (16048)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)
% 0.14/0.39  % (16047)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39  % (16051)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)
% 0.14/0.39  % (16049)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39  % (16052)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)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  % (16046)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40  TRYING [3]
% 0.14/0.40  TRYING [1]
% 0.14/0.40  TRYING [2]
% 0.14/0.42  TRYING [4]
% 0.14/0.42  TRYING [3]
% 0.22/0.47  TRYING [4]
% 0.22/0.50  TRYING [5]
% 2.78/0.82  % (16052)First to succeed.
% 2.78/0.82  % (16052)Refutation found. Thanks to Tanya!
% 2.78/0.82  % SZS status Theorem for theBenchmark
% 2.78/0.82  % SZS output start Proof for theBenchmark
% See solution above
% 2.78/0.82  % (16052)------------------------------
% 2.78/0.82  % (16052)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.78/0.82  % (16052)Termination reason: Refutation
% 2.78/0.82  
% 2.78/0.82  % (16052)Memory used [KB]: 5553
% 2.78/0.82  % (16052)Time elapsed: 0.433 s
% 2.78/0.82  % (16052)Instructions burned: 929 (million)
% 2.78/0.82  % (16052)------------------------------
% 2.78/0.82  % (16052)------------------------------
% 2.78/0.82  % (16045)Success in time 0.448 s
%------------------------------------------------------------------------------