TSTP Solution File: SWW235+1 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SWW235+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n020.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 18:31:41 EDT 2024

% Result   : Theorem 0.21s 0.51s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   28 (  14 unt;   0 def)
%            Number of atoms       :   42 (   8 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   30 (  16   ~;   8   |;   0   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-3 aty)
%            Number of variables   :   40 (  40   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3988,plain,
    $false,
    inference(subsumption_resolution,[],[f3984,f2949]) ).

fof(f2949,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1170]) ).

fof(f1170,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f3984,plain,
    ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(resolution,[],[f3859,f2977]) ).

fof(f2977,plain,
    ! [X2,X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(cnf_transformation,[],[f2122]) ).

fof(f2122,plain,
    ! [X0,X1,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0)))
      | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(ennf_transformation,[],[f1430]) ).

fof(f1430,plain,
    ! [X0,X1,X2] :
      ( class_RealVector_Oreal__normed__vector(X2)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X0)),c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0))) ),
    inference(rectify,[],[f48]) ).

fof(f48,axiom,
    ! [X3,X4,X5] :
      ( class_RealVector_Oreal__normed__vector(X5)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5,X4),c_RealVector_Onorm__class_Onorm(X5,X3)),c_RealVector_Onorm__class_Onorm(X5,c_Groups_Oplus__class_Oplus(X5,X4,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f3859,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____)),v_aa____))),
    inference(subsumption_resolution,[],[f3856,f2948]) ).

fof(f2948,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1178]) ).

fof(f1178,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f3856,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____)),v_aa____)))
    | ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    inference(superposition,[],[f3814,f3336]) ).

fof(f3336,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(cnf_transformation,[],[f2352]) ).

fof(f2352,plain,
    ! [X0,X1,X2] :
      ( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
      | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(ennf_transformation,[],[f1697]) ).

fof(f1697,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__1(X2)
     => c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
    inference(rectify,[],[f227]) ).

fof(f227,axiom,
    ! [X21,X4,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => c_Groups_Oplus__class_Oplus(X5,X4,X21) = c_Groups_Oplus__class_Oplus(X5,X21,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f3814,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____))))),
    inference(subsumption_resolution,[],[f3812,f3400]) ).

fof(f3400,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(cnf_transformation,[],[f1179]) ).

fof(f1179,axiom,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f3812,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_aa____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____)))))
    | ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
    inference(superposition,[],[f2712,f2957]) ).

fof(f2957,plain,
    ! [X2,X3,X0,X1] :
      ( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f2106]) ).

fof(f2106,plain,
    ! [X0,X1,X2,X3] :
      ( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(ennf_transformation,[],[f1419]) ).

fof(f1419,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__0(X3)
     => hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))) ),
    inference(rectify,[],[f49]) ).

fof(f49,axiom,
    ! [X8,X10,X4,X5] :
      ( class_Rings_Ocomm__semiring__0(X5)
     => hAPP(c_Polynomial_Opoly(X5,c_Polynomial_OpCons(X5,X4,X10)),X8) = c_Groups_Oplus__class_Oplus(X5,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X8),hAPP(c_Polynomial_Opoly(X5,X10),X8))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f2712,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_aa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____))),v_z____))),
    inference(cnf_transformation,[],[f1261]) ).

fof(f1261,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_aa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____))),v_z____))),
    inference(flattening,[],[f1260]) ).

fof(f1260,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_aa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____))),v_z____))),
    inference(negated_conjecture,[],[f1259]) ).

fof(f1259,conjecture,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_aa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____))),v_z____))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWW235+1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Wed Jun 19 09:09:09 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.21/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.21/0.36  Running first-order theorem proving
% 0.21/0.36  Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47  % (16744)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.47  % (16751)lrs+1002_1:1_to=lpo:sil=2000:sp=frequency:sos=on:st=3.0:i=282:sd=2:ss=axioms_0 on theBenchmark for (2999ds/282Mi)
% 0.21/0.47  % (16744)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.47  % (16750)lrs-1011_8:1_sil=16000:sos=all:i=346:sd=1:ep=R:ss=axioms_0 on theBenchmark for (2999ds/346Mi)
% 0.21/0.48  % (16744)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.48  % (16745)lrs+10_1:628_anc=all_dependent:bsr=unit_only:sil=256000:sp=frequency:i=136310:newcnf=on_0 on theBenchmark for (2999ds/136310Mi)
% 0.21/0.48  % (16744)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.48  % (16748)dis+2_1:50_sil=256000:flr=on:sac=on:i=218245:fsr=off:uhcvi=on_0 on theBenchmark for (2999ds/218245Mi)
% 0.21/0.48  % (16744)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.48  % (16749)lrs-1010_1:1_sil=2000:i=250:sd=1:ss=axioms:sgt=32:sos=on_0 on theBenchmark for (2999ds/250Mi)
% 0.21/0.48  % (16744)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.48  % (16746)lrs+2_3:1_to=lpo:sil=256000:irw=on:fde=unused:sp=unary_first:bce=on:nwc=6.0:s2agt=30:newcnf=on:s2a=on:i=140573:nm=2_0 on theBenchmark for (2999ds/140573Mi)
% 0.21/0.48  % (16744)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.48  % (16747)lrs+11_1:12_to=lpo:sil=128000:sp=const_min:i=103397:ss=included:sgt=16:av=off:fsd=on:nm=16_0 on theBenchmark for (2999ds/103397Mi)
% 0.21/0.51  % (16751)First to succeed.
% 0.21/0.51  % (16751)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16744"
% 0.21/0.51  % (16744)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.51  % (16751)Refutation found. Thanks to Tanya!
% 0.21/0.51  % SZS status Theorem for theBenchmark
% 0.21/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51  % (16751)------------------------------
% 0.21/0.51  % (16751)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.51  % (16751)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.51  % (16751)Termination reason: Refutation
% 0.21/0.51  
% 0.21/0.51  % (16751)Memory used [KB]: 4044
% 0.21/0.51  % (16751)Time elapsed: 0.041 s
% 0.21/0.51  % (16751)Instructions burned: 123 (million)
% 0.21/0.51  % (16751)------------------------------
% 0.21/0.51  % (16751)------------------------------
% 0.21/0.51  % (16744)Success in time 0.082 s
%------------------------------------------------------------------------------