TSTP Solution File: GRP704+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP704+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n031.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 20:21:28 EDT 2024

% Result   : Theorem 4.37s 0.92s
% Output   : CNFRefutation 4.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   67 (  40 unt;   0 def)
%            Number of atoms       :  101 (  71 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   64 (  30   ~;  27   |;   4   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   4 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  11 con; 0-2 aty)
%            Number of variables   :   72 (  64   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [B,A] : mult(A,ld(A,B)) = B,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [B,A] : ld(A,mult(A,B)) = B,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [B,A] : mult(rd(A,B),B) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [A] : mult(A,unit) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [C,B,A] : mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [B,A] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [B,A] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [B,A] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [A] : op_d = ld(A,mult(op_c,A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [B,A] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [B,A] : op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,conjecture,
    ! [X4,X5] :
      ( mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5)
      & mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)
      & mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,negated_conjecture,
    ~ ! [X4,X5] :
        ( mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5)
        & mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)
        & mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5) ),
    inference(negated_conjecture,[status(cth)],[f14]) ).

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

fof(f17,plain,
    ! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f18,plain,
    ! [X0,X1] : mult(rd(X0,X1),X1) = X0,
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f20,plain,
    ! [X0] : mult(X0,unit) = X0,
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f22,plain,
    ! [X0,X1,X2] : mult(X0,mult(X1,mult(X1,X2))) = mult(mult(mult(X0,X1),X1),X2),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f23,plain,
    ! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f24,plain,
    ! [X0,X1] : mult(X0,mult(X1,op_c)) = mult(mult(X0,X1),op_c),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f25,plain,
    ! [X0,X1] : mult(X0,mult(op_c,X1)) = mult(mult(X0,op_c),X1),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f26,plain,
    ! [X0] : op_d = ld(X0,mult(op_c,X0)),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f27,plain,
    ! [X0,X1] : op_e = mult(mult(rd(op_c,mult(X0,X1)),X1),X0),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f28,plain,
    ! [X0,X1] : op_f = mult(X0,mult(X1,ld(mult(X0,X1),op_c))),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f29,plain,
    ? [X4,X5] :
      ( mult(op_f,mult(X4,X5)) != mult(mult(op_f,X4),X5)
      | mult(X4,mult(X5,op_f)) != mult(mult(X4,X5),op_f)
      | mult(X4,mult(op_f,X5)) != mult(mult(X4,op_f),X5) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f30,plain,
    ( ? [X4,X5] : mult(op_f,mult(X4,X5)) != mult(mult(op_f,X4),X5)
    | ? [X4,X5] : mult(X4,mult(X5,op_f)) != mult(mult(X4,X5),op_f)
    | ? [X4,X5] : mult(X4,mult(op_f,X5)) != mult(mult(X4,op_f),X5) ),
    inference(miniscoping,[status(esa)],[f29]) ).

fof(f31,plain,
    ( mult(op_f,mult(sk0_0,sk0_1)) != mult(mult(op_f,sk0_0),sk0_1)
    | mult(sk0_2,mult(sk0_3,op_f)) != mult(mult(sk0_2,sk0_3),op_f)
    | mult(sk0_4,mult(op_f,sk0_5)) != mult(mult(sk0_4,op_f),sk0_5) ),
    inference(skolemization,[status(esa)],[f30]) ).

fof(f32,plain,
    ( mult(op_f,mult(sk0_0,sk0_1)) != mult(mult(op_f,sk0_0),sk0_1)
    | mult(sk0_2,mult(sk0_3,op_f)) != mult(mult(sk0_2,sk0_3),op_f)
    | mult(sk0_4,mult(op_f,sk0_5)) != mult(mult(sk0_4,op_f),sk0_5) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f33,plain,
    ( spl0_0
  <=> mult(op_f,mult(sk0_0,sk0_1)) = mult(mult(op_f,sk0_0),sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f35,plain,
    ( mult(op_f,mult(sk0_0,sk0_1)) != mult(mult(op_f,sk0_0),sk0_1)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f33]) ).

fof(f36,plain,
    ( spl0_1
  <=> mult(sk0_2,mult(sk0_3,op_f)) = mult(mult(sk0_2,sk0_3),op_f) ),
    introduced(split_symbol_definition) ).

fof(f38,plain,
    ( mult(sk0_2,mult(sk0_3,op_f)) != mult(mult(sk0_2,sk0_3),op_f)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f36]) ).

fof(f39,plain,
    ( spl0_2
  <=> mult(sk0_4,mult(op_f,sk0_5)) = mult(mult(sk0_4,op_f),sk0_5) ),
    introduced(split_symbol_definition) ).

fof(f41,plain,
    ( mult(sk0_4,mult(op_f,sk0_5)) != mult(mult(sk0_4,op_f),sk0_5)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f39]) ).

fof(f42,plain,
    ( ~ spl0_0
    | ~ spl0_1
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f32,f33,f36,f39]) ).

fof(f3279,plain,
    ! [X0,X1] : mult(X0,mult(X1,mult(X1,unit))) = mult(mult(X0,X1),X1),
    inference(paramodulation,[status(thm)],[f22,f20]) ).

fof(f3280,plain,
    ! [X0,X1] : mult(X0,mult(X1,X1)) = mult(mult(X0,X1),X1),
    inference(forward_demodulation,[status(thm)],[f20,f3279]) ).

fof(f3820,plain,
    ! [X0] : ld(X0,X0) = unit,
    inference(paramodulation,[status(thm)],[f20,f17]) ).

fof(f4971,plain,
    ! [X0,X1] : ld(mult(X0,X1),mult(X0,mult(X1,X1))) = X1,
    inference(paramodulation,[status(thm)],[f3280,f17]) ).

fof(f5822,plain,
    op_d = op_c,
    inference(paramodulation,[status(thm)],[f26,f4971]) ).

fof(f5902,plain,
    ! [X0] : op_c = ld(X0,mult(op_c,X0)),
    inference(backward_demodulation,[status(thm)],[f5822,f26]) ).

fof(f5908,plain,
    ! [X0] : mult(X0,op_c) = mult(op_c,X0),
    inference(paramodulation,[status(thm)],[f5902,f16]) ).

fof(f6090,plain,
    ! [X0] : op_e = mult(rd(op_c,mult(X0,X0)),mult(X0,X0)),
    inference(paramodulation,[status(thm)],[f3280,f27]) ).

fof(f6091,plain,
    op_e = op_c,
    inference(forward_demodulation,[status(thm)],[f18,f6090]) ).

fof(f6577,plain,
    ! [X0,X1] : op_c = mult(mult(rd(op_c,mult(X0,X1)),X1),X0),
    inference(backward_demodulation,[status(thm)],[f6091,f27]) ).

fof(f6683,plain,
    ! [X0,X1] : op_f = mult(mult(rd(op_c,mult(X0,X1)),X1),mult(X0,ld(op_c,op_c))),
    inference(paramodulation,[status(thm)],[f6577,f28]) ).

fof(f6684,plain,
    ! [X0,X1] : op_f = mult(mult(rd(op_c,mult(X0,X1)),X1),mult(X0,unit)),
    inference(forward_demodulation,[status(thm)],[f3820,f6683]) ).

fof(f6685,plain,
    ! [X0,X1] : op_f = mult(mult(rd(op_c,mult(X0,X1)),X1),X0),
    inference(forward_demodulation,[status(thm)],[f20,f6684]) ).

fof(f6686,plain,
    op_f = op_c,
    inference(forward_demodulation,[status(thm)],[f6577,f6685]) ).

fof(f6717,plain,
    ( mult(sk0_4,mult(op_f,sk0_5)) != mult(mult(sk0_4,op_c),sk0_5)
    | spl0_2 ),
    inference(backward_demodulation,[status(thm)],[f6686,f41]) ).

fof(f6718,plain,
    ( mult(sk0_4,mult(op_c,sk0_5)) != mult(mult(sk0_4,op_c),sk0_5)
    | spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f6686,f6717]) ).

fof(f6719,plain,
    ( mult(sk0_4,mult(op_c,sk0_5)) != mult(sk0_4,mult(op_c,sk0_5))
    | spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f25,f6718]) ).

fof(f6720,plain,
    ( $false
    | spl0_2 ),
    inference(trivial_equality_resolution,[status(esa)],[f6719]) ).

fof(f6721,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f6720]) ).

fof(f6722,plain,
    ( mult(op_c,mult(sk0_0,sk0_1)) != mult(mult(op_f,sk0_0),sk0_1)
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f6686,f35]) ).

fof(f6723,plain,
    ( mult(op_c,mult(sk0_0,sk0_1)) != mult(mult(op_c,sk0_0),sk0_1)
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f6686,f6722]) ).

fof(f6724,plain,
    ( mult(op_c,mult(sk0_0,sk0_1)) != mult(op_c,mult(sk0_0,sk0_1))
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f23,f6723]) ).

fof(f6725,plain,
    ( $false
    | spl0_0 ),
    inference(trivial_equality_resolution,[status(esa)],[f6724]) ).

fof(f6726,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f6725]) ).

fof(f6729,plain,
    ( mult(sk0_2,mult(sk0_3,op_c)) != mult(mult(sk0_2,sk0_3),op_f)
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f6686,f38]) ).

fof(f6730,plain,
    ( mult(sk0_2,mult(op_c,sk0_3)) != mult(mult(sk0_2,sk0_3),op_f)
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f5908,f6729]) ).

fof(f6731,plain,
    ( mult(sk0_2,mult(op_c,sk0_3)) != mult(mult(sk0_2,sk0_3),op_c)
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f6686,f6730]) ).

fof(f6732,plain,
    ( mult(sk0_2,mult(op_c,sk0_3)) != mult(sk0_2,mult(sk0_3,op_c))
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f24,f6731]) ).

fof(f6733,plain,
    ( mult(sk0_2,mult(op_c,sk0_3)) != mult(sk0_2,mult(op_c,sk0_3))
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f5908,f6732]) ).

fof(f6734,plain,
    ( $false
    | spl0_1 ),
    inference(trivial_equality_resolution,[status(esa)],[f6733]) ).

fof(f6735,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f6734]) ).

fof(f6736,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f42,f6721,f6726,f6735]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP704+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n031.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 : Tue Apr 30 01:07:58 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 4.37/0.92  % Refutation found
% 4.37/0.92  % SZS status Theorem for theBenchmark: Theorem is valid
% 4.37/0.92  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.51/0.95  % Elapsed time: 0.597390 seconds
% 4.51/0.95  % CPU time: 4.628667 seconds
% 4.51/0.95  % Total memory used: 195.584 MB
% 4.51/0.95  % Net memory used: 194.202 MB
%------------------------------------------------------------------------------