TSTP Solution File: GRP682-11 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP682-11 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.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 20:21:23 EDT 2024

% Result   : Unsatisfiable 0.19s 0.52s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :    8
% Syntax   : Number of formulae    :  102 ( 102 unt;   0 def)
%            Number of atoms       :  102 ( 101 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    9 (   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   :  225 ( 225   !;   0   ?)

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

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

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

fof(f4,axiom,
    ! [A,B] : mult(rd(A,B),B) = rd(mult(A,B),B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f6,axiom,
    ! [A,B,C,D] : rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f8,negated_conjecture,
    ld(rd(x0,x1),mult(rd(x0,x1),x2)) != ld(x0,mult(x0,x2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,plain,
    ! [X0] : ld(X0,mult(X0,X0)) = X0,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f10,plain,
    ! [X0] : rd(mult(X0,X0),X0) = X0,
    inference(cnf_transformation,[status(esa)],[f2]) ).

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

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

fof(f13,plain,
    ! [X0,X1,X2,X3] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
    inference(cnf_transformation,[status(esa)],[f5]) ).

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

fof(f15,plain,
    ! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f16,plain,
    ld(rd(x0,x1),mult(rd(x0,x1),x2)) != ld(x0,mult(x0,x2)),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f17,plain,
    ! [X0,X1,X2,X3] : mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
    inference(forward_demodulation,[status(thm)],[f11,f13]) ).

fof(f18,plain,
    ! [X0,X1,X2,X3] : mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
    inference(forward_demodulation,[status(thm)],[f11,f17]) ).

fof(f19,plain,
    ! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
    inference(forward_demodulation,[status(thm)],[f12,f14]) ).

fof(f20,plain,
    ! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,mult(rd(X1,X3),X3)),
    inference(forward_demodulation,[status(thm)],[f12,f19]) ).

fof(f21,plain,
    ! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
    inference(forward_demodulation,[status(thm)],[f11,f15]) ).

fof(f22,plain,
    ! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(rd(rd(X0,X0),X1),X1),
    inference(forward_demodulation,[status(thm)],[f12,f21]) ).

fof(f23,plain,
    mult(rd(x0,x1),ld(rd(x0,x1),x2)) != ld(x0,mult(x0,x2)),
    inference(forward_demodulation,[status(thm)],[f11,f16]) ).

fof(f24,plain,
    mult(rd(x0,x1),ld(rd(x0,x1),x2)) != mult(x0,ld(x0,x2)),
    inference(forward_demodulation,[status(thm)],[f11,f23]) ).

fof(f25,plain,
    ! [X0] : mult(X0,ld(X0,X0)) = X0,
    inference(backward_demodulation,[status(thm)],[f11,f9]) ).

fof(f26,plain,
    ! [X0] : mult(rd(X0,X0),X0) = X0,
    inference(backward_demodulation,[status(thm)],[f12,f10]) ).

fof(f28,plain,
    ! [X0] : mult(X0,ld(X0,ld(X0,X0))) = ld(X0,X0),
    inference(paramodulation,[status(thm)],[f25,f11]) ).

fof(f29,plain,
    ! [X0] : mult(rd(rd(X0,X0),X0),X0) = rd(X0,X0),
    inference(paramodulation,[status(thm)],[f26,f12]) ).

fof(f30,plain,
    ! [X0] : mult(X0,ld(X0,ld(X0,X0))) = rd(X0,X0),
    inference(forward_demodulation,[status(thm)],[f22,f29]) ).

fof(f31,plain,
    ! [X0] : ld(X0,X0) = rd(X0,X0),
    inference(forward_demodulation,[status(thm)],[f28,f30]) ).

fof(f32,plain,
    ! [X0] : mult(rd(X0,ld(X0,X0)),ld(X0,X0)) = rd(X0,ld(X0,X0)),
    inference(paramodulation,[status(thm)],[f25,f12]) ).

fof(f33,plain,
    ! [X0] : mult(ld(X0,X0),X0) = X0,
    inference(backward_demodulation,[status(thm)],[f31,f26]) ).

fof(f36,plain,
    ! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(rd(ld(X0,X0),X1),X1),
    inference(backward_demodulation,[status(thm)],[f31,f22]) ).

fof(f37,plain,
    ! [X0,X1,X2,X3] : mult(mult(X0,ld(X0,X1)),ld(ld(X0,mult(X0,X1)),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
    inference(paramodulation,[status(thm)],[f11,f18]) ).

fof(f38,plain,
    ! [X0,X1,X2,X3] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
    inference(forward_demodulation,[status(thm)],[f11,f37]) ).

fof(f44,plain,
    ! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(mult(X0,ld(X0,X2)),ld(X2,X2)),
    inference(paramodulation,[status(thm)],[f25,f18]) ).

fof(f59,plain,
    ! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = mult(ld(ld(X0,X0),ld(X0,X0)),ld(X0,X0)),
    inference(paramodulation,[status(thm)],[f31,f36]) ).

fof(f60,plain,
    ! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = ld(X0,X0),
    inference(forward_demodulation,[status(thm)],[f33,f59]) ).

fof(f91,plain,
    ! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(ld(X0,X0),X2),X2)),
    inference(paramodulation,[status(thm)],[f25,f20]) ).

fof(f92,plain,
    ! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(X0,ld(X0,ld(X2,X2)))),
    inference(forward_demodulation,[status(thm)],[f36,f91]) ).

fof(f138,plain,
    ! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),ld(X1,X1))) = ld(mult(X0,ld(X0,X1)),mult(ld(X0,X2),ld(ld(X0,X2),X1))),
    inference(paramodulation,[status(thm)],[f44,f11]) ).

fof(f177,plain,
    ! [X0,X1,X2] : mult(X0,ld(mult(X0,ld(X0,X0)),mult(X1,X2))) = mult(mult(X0,ld(X0,X1)),X2),
    inference(paramodulation,[status(thm)],[f25,f38]) ).

fof(f178,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,X2))) = mult(mult(X0,ld(X0,X1)),X2),
    inference(forward_demodulation,[status(thm)],[f25,f177]) ).

fof(f273,plain,
    ! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2)) = mult(mult(X0,ld(X0,ld(X2,X2))),X2),
    inference(paramodulation,[status(thm)],[f33,f38]) ).

fof(f274,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(mult(X0,ld(X0,ld(X2,X2))),X2),
    inference(forward_demodulation,[status(thm)],[f178,f273]) ).

fof(f275,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(X0,ld(X0,mult(ld(X2,X2),X2))),
    inference(forward_demodulation,[status(thm)],[f178,f274]) ).

fof(f276,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(X0,ld(X0,X2)),
    inference(forward_demodulation,[status(thm)],[f33,f275]) ).

fof(f296,plain,
    ! [X0,X1] : mult(mult(X0,ld(X0,X0)),ld(X0,X1)) = mult(X0,ld(X0,X1)),
    inference(paramodulation,[status(thm)],[f38,f25]) ).

fof(f297,plain,
    ! [X0,X1] : mult(X0,ld(X0,mult(X0,ld(X0,X1)))) = mult(X0,ld(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f178,f296]) ).

fof(f298,plain,
    ! [X0,X1] : mult(X0,mult(X0,ld(X0,ld(X0,X1)))) = mult(X0,ld(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f11,f297]) ).

fof(f311,plain,
    ! [X0,X1,X2,X3] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),mult(X2,X3)))) = ld(mult(X0,ld(X0,X1)),mult(mult(X0,ld(X0,X2)),X3)),
    inference(paramodulation,[status(thm)],[f38,f11]) ).

fof(f312,plain,
    ! [X0,X1,X2,X3] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),mult(X2,X3)))))) = ld(mult(X0,ld(X0,X1)),mult(mult(X0,ld(X0,X2)),X3)),
    inference(forward_demodulation,[status(thm)],[f178,f311]) ).

fof(f313,plain,
    ! [X0,X1,X2,X3] : mult(X0,ld(X0,ld(mult(X0,ld(X0,X1)),mult(X2,X3)))) = ld(mult(X0,ld(X0,X1)),mult(mult(X0,ld(X0,X2)),X3)),
    inference(forward_demodulation,[status(thm)],[f276,f312]) ).

fof(f314,plain,
    ! [X0,X1,X2,X3] : mult(X0,ld(X0,ld(mult(X0,ld(X0,X1)),mult(X2,X3)))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X2,X3)))),
    inference(forward_demodulation,[status(thm)],[f178,f313]) ).

fof(f317,plain,
    ! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,mult(X2,ld(X2,X2)))),
    inference(backward_demodulation,[status(thm)],[f178,f44]) ).

fof(f318,plain,
    ! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,X2)),
    inference(forward_demodulation,[status(thm)],[f25,f317]) ).

fof(f366,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),ld(X1,X1))))) = ld(mult(X0,ld(X0,X1)),mult(ld(X0,X2),ld(ld(X0,X2),X1))),
    inference(backward_demodulation,[status(thm)],[f178,f138]) ).

fof(f367,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,ld(X1,X1))) = ld(mult(X0,ld(X0,X1)),mult(ld(X0,X2),ld(ld(X0,X2),X1))),
    inference(forward_demodulation,[status(thm)],[f276,f366]) ).

fof(f368,plain,
    ! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f318,f367]) ).

fof(f416,plain,
    ! [X0,X1] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),ld(ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1)))))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
    inference(paramodulation,[status(thm)],[f60,f178]) ).

fof(f417,plain,
    ! [X0,X1] : mult(X0,ld(X0,ld(ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1)))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f276,f416]) ).

fof(f418,plain,
    ! [X0,X1] : mult(X0,ld(X0,ld(mult(X0,ld(X0,ld(X1,X1))),ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1)))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f368,f417]) ).

fof(f419,plain,
    ! [X0,X1] : mult(X0,ld(X0,ld(mult(X0,ld(X0,ld(X1,X1))),mult(X0,ld(X0,ld(X1,X1)))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f368,f418]) ).

fof(f420,plain,
    ! [X0,X1] : mult(X0,ld(X0,mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f368,f419]) ).

fof(f421,plain,
    ! [X0,X1] : mult(X0,mult(X0,ld(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f11,f420]) ).

fof(f422,plain,
    ! [X0,X1] : mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f298,f421]) ).

fof(f423,plain,
    ! [X0,X1] : mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))) = mult(X0,ld(X0,ld(X1,X1))),
    inference(forward_demodulation,[status(thm)],[f368,f422]) ).

fof(f438,plain,
    ! [X0,X1] : mult(X0,ld(X0,mult(X0,X1))) = mult(X0,X1),
    inference(paramodulation,[status(thm)],[f25,f178]) ).

fof(f439,plain,
    ! [X0,X1] : mult(X0,mult(X0,ld(X0,X1))) = mult(X0,X1),
    inference(forward_demodulation,[status(thm)],[f11,f438]) ).

fof(f468,plain,
    ! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2)) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))),
    inference(paramodulation,[status(thm)],[f178,f11]) ).

fof(f469,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))),
    inference(forward_demodulation,[status(thm)],[f178,f468]) ).

fof(f470,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,X1)) = ld(mult(X0,ld(X0,X2)),mult(X0,ld(X0,mult(X2,X1)))),
    inference(forward_demodulation,[status(thm)],[f276,f469]) ).

fof(f471,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,X1)) = mult(X0,ld(X0,ld(mult(X0,ld(X0,X2)),mult(X2,X1)))),
    inference(forward_demodulation,[status(thm)],[f314,f470]) ).

fof(f477,plain,
    ! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,ld(X2,X2)),
    inference(backward_demodulation,[status(thm)],[f439,f92]) ).

fof(f509,plain,
    ! [X0,X1] : ld(X0,X1) = mult(X0,ld(X0,ld(X0,X1))),
    inference(paramodulation,[status(thm)],[f25,f318]) ).

fof(f541,plain,
    ! [X0,X1,X2] : ld(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2))))),
    inference(paramodulation,[status(thm)],[f178,f509]) ).

fof(f542,plain,
    ! [X0,X1,X2] : ld(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,ld(mult(X0,ld(X0,X1)),X2))),
    inference(forward_demodulation,[status(thm)],[f276,f541]) ).

fof(f557,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,X1)) = ld(mult(X0,ld(X0,X2)),mult(X2,X1)),
    inference(backward_demodulation,[status(thm)],[f542,f471]) ).

fof(f579,plain,
    ! [X0,X1] : mult(ld(rd(X0,X1),rd(X0,X1)),rd(X0,X1)) = mult(rd(X0,X1),ld(X1,X1)),
    inference(paramodulation,[status(thm)],[f31,f477]) ).

fof(f580,plain,
    ! [X0,X1] : rd(X0,X1) = mult(rd(X0,X1),ld(X1,X1)),
    inference(forward_demodulation,[status(thm)],[f33,f579]) ).

fof(f587,plain,
    ! [X0,X1] : mult(rd(X0,ld(X1,X1)),rd(X1,X1)) = mult(X0,ld(X1,X1)),
    inference(paramodulation,[status(thm)],[f31,f477]) ).

fof(f588,plain,
    ! [X0,X1] : mult(rd(X0,ld(X1,X1)),ld(X1,X1)) = mult(X0,ld(X1,X1)),
    inference(forward_demodulation,[status(thm)],[f31,f587]) ).

fof(f608,plain,
    ! [X0] : mult(X0,ld(X0,X0)) = rd(X0,ld(X0,X0)),
    inference(backward_demodulation,[status(thm)],[f588,f32]) ).

fof(f609,plain,
    ! [X0] : X0 = rd(X0,ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f25,f608]) ).

fof(f629,plain,
    ! [X0,X1] : mult(rd(X0,rd(X1,ld(X1,X1))),X1) = mult(X0,ld(ld(X1,X1),ld(X1,X1))),
    inference(paramodulation,[status(thm)],[f609,f477]) ).

fof(f630,plain,
    ! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,ld(ld(X1,X1),ld(X1,X1))),
    inference(forward_demodulation,[status(thm)],[f609,f629]) ).

fof(f645,plain,
    ! [X0] : rd(X0,X0) = mult(ld(X0,X0),ld(X0,X0)),
    inference(paramodulation,[status(thm)],[f31,f580]) ).

fof(f646,plain,
    ! [X0] : ld(X0,X0) = mult(ld(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f31,f645]) ).

fof(f651,plain,
    ! [X0] : mult(rd(ld(X0,X0),ld(X0,X0)),ld(X0,X0)) = rd(ld(X0,X0),ld(X0,X0)),
    inference(paramodulation,[status(thm)],[f646,f12]) ).

fof(f652,plain,
    ! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = rd(ld(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f36,f651]) ).

fof(f653,plain,
    ! [X0] : mult(X0,ld(X0,ld(X0,X0))) = rd(ld(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f423,f652]) ).

fof(f654,plain,
    ! [X0] : ld(X0,X0) = rd(ld(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f509,f653]) ).

fof(f655,plain,
    ! [X0] : ld(X0,X0) = ld(ld(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f31,f654]) ).

fof(f659,plain,
    ! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,ld(X1,X1)),
    inference(backward_demodulation,[status(thm)],[f655,f630]) ).

fof(f823,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,X1)) = ld(mult(X0,mult(X0,ld(X0,X2))),mult(mult(X0,X2),X1)),
    inference(paramodulation,[status(thm)],[f11,f557]) ).

fof(f824,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,X1)) = ld(mult(X0,X2),mult(mult(X0,X2),X1)),
    inference(forward_demodulation,[status(thm)],[f439,f823]) ).

fof(f825,plain,
    ! [X0,X1,X2] : mult(X0,ld(X0,X1)) = mult(mult(X0,X2),ld(mult(X0,X2),X1)),
    inference(forward_demodulation,[status(thm)],[f11,f824]) ).

fof(f1773,plain,
    ! [X0,X1,X2] : mult(rd(X0,X1),ld(rd(X0,X1),X2)) = mult(mult(X0,ld(X1,X1)),ld(mult(rd(X0,X1),X1),X2)),
    inference(paramodulation,[status(thm)],[f659,f825]) ).

fof(f1774,plain,
    ! [X0,X1,X2] : mult(rd(X0,X1),ld(rd(X0,X1),X2)) = mult(mult(X0,ld(X1,X1)),ld(mult(X0,ld(X1,X1)),X2)),
    inference(forward_demodulation,[status(thm)],[f659,f1773]) ).

fof(f1775,plain,
    ! [X0,X1,X2] : mult(rd(X0,X1),ld(rd(X0,X1),X2)) = mult(X0,ld(X0,X2)),
    inference(forward_demodulation,[status(thm)],[f825,f1774]) ).

fof(f1886,plain,
    mult(x0,ld(x0,x2)) != mult(x0,ld(x0,x2)),
    inference(backward_demodulation,[status(thm)],[f1775,f24]) ).

fof(f1887,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f1886]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem  : GRP682-11 : TPTP v8.1.2. Released v8.1.0.
% 0.04/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n006.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Tue Apr 30 00:25:35 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.11/0.33  % Drodi V3.6.0
% 0.19/0.52  % Refutation found
% 0.19/0.52  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.52  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.52  % Elapsed time: 0.192105 seconds
% 0.19/0.52  % CPU time: 1.465755 seconds
% 0.19/0.52  % Total memory used: 41.131 MB
% 0.19/0.52  % Net memory used: 38.859 MB
%------------------------------------------------------------------------------