TSTP Solution File: GRP486-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP486-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%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 : Tue Apr 30 20:20:46 EDT 2024

% Result   : Unsatisfiable 0.20s 0.47s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   93 (  93 unt;   0 def)
%            Number of atoms       :   93 (  92 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  178 ( 178   !;   0   ?)

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

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

fof(f3,axiom,
    ! [A] : inverse(A) = double_divide(A,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A] : identity = double_divide(A,inverse(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,negated_conjecture,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,plain,
    ! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(X0,X1),X2),double_divide(X1,identity))),double_divide(identity,identity)) = X2,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f7,plain,
    ! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f8,plain,
    ! [X0] : inverse(X0) = double_divide(X0,identity),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f9,plain,
    ! [X0] : identity = double_divide(X0,inverse(X0)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f10,plain,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f11,plain,
    ! [X0,X1] : multiply(identity,double_divide(X0,X1)) = double_divide(multiply(X1,X0),identity),
    inference(paramodulation,[status(thm)],[f7,f7]) ).

fof(f14,plain,
    ! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
    inference(backward_demodulation,[status(thm)],[f8,f7]) ).

fof(f15,plain,
    ! [X0,X1] : multiply(identity,double_divide(X0,X1)) = inverse(multiply(X1,X0)),
    inference(backward_demodulation,[status(thm)],[f8,f11]) ).

fof(f16,plain,
    ! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
    inference(paramodulation,[status(thm)],[f8,f14]) ).

fof(f17,plain,
    ! [X0] : inverse(multiply(identity,X0)) = multiply(identity,inverse(X0)),
    inference(paramodulation,[status(thm)],[f8,f15]) ).

fof(f25,plain,
    ! [X0] : identity = double_divide(inverse(X0),multiply(identity,X0)),
    inference(paramodulation,[status(thm)],[f16,f9]) ).

fof(f26,plain,
    ! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
    inference(paramodulation,[status(thm)],[f14,f9]) ).

fof(f28,plain,
    ! [X0] : multiply(inverse(X0),X0) = inverse(identity),
    inference(paramodulation,[status(thm)],[f9,f14]) ).

fof(f30,plain,
    ! [X0] : inverse(identity) = multiply(multiply(identity,X0),inverse(X0)),
    inference(paramodulation,[status(thm)],[f16,f28]) ).

fof(f114,plain,
    ! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(X0,X1),X2),inverse(X1))),double_divide(identity,identity)) = X2,
    inference(forward_demodulation,[status(thm)],[f8,f6]) ).

fof(f115,plain,
    ! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(X0,X1),X2),inverse(X1))),inverse(identity)) = X2,
    inference(forward_demodulation,[status(thm)],[f8,f114]) ).

fof(f116,plain,
    ! [X0,X1,X2] : double_divide(double_divide(double_divide(double_divide(X0,identity),X1),X2),inverse(X1)) = double_divide(double_divide(X0,X2),inverse(identity)),
    inference(paramodulation,[status(thm)],[f115,f115]) ).

fof(f118,plain,
    ! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,double_divide(identity,inverse(X0))),inverse(identity)),
    inference(paramodulation,[status(thm)],[f26,f115]) ).

fof(f120,plain,
    ! [X0,X1] : identity = double_divide(double_divide(X0,double_divide(inverse(double_divide(X0,X1)),inverse(X1))),inverse(identity)),
    inference(paramodulation,[status(thm)],[f8,f115]) ).

fof(f123,plain,
    ! [X0,X1,X2,X3] : X0 = double_divide(double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),double_divide(double_divide(X3,X0),inverse(inverse(identity)))),inverse(identity)),
    inference(paramodulation,[status(thm)],[f115,f115]) ).

fof(f126,plain,
    ! [X0,X1] : X0 = double_divide(double_divide(X1,double_divide(double_divide(identity,X0),inverse(inverse(X1)))),inverse(identity)),
    inference(paramodulation,[status(thm)],[f9,f115]) ).

fof(f127,plain,
    ! [X0,X1] : X0 = double_divide(double_divide(X1,double_divide(double_divide(inverse(X1),X0),inverse(identity))),inverse(identity)),
    inference(paramodulation,[status(thm)],[f8,f115]) ).

fof(f135,plain,
    ! [X0,X1,X2] : double_divide(double_divide(double_divide(inverse(X0),X1),X2),inverse(X1)) = double_divide(double_divide(X0,X2),inverse(identity)),
    inference(forward_demodulation,[status(thm)],[f8,f116]) ).

fof(f138,plain,
    ! [X0,X1] : identity = double_divide(double_divide(X0,double_divide(multiply(X1,X0),inverse(X1))),inverse(identity)),
    inference(forward_demodulation,[status(thm)],[f14,f120]) ).

fof(f143,plain,
    ! [X0,X1,X2,X3] : X0 = double_divide(double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),double_divide(double_divide(X3,X0),multiply(identity,identity))),inverse(identity)),
    inference(forward_demodulation,[status(thm)],[f16,f123]) ).

fof(f145,plain,
    ! [X0,X1] : X0 = double_divide(double_divide(X1,double_divide(double_divide(identity,X0),multiply(identity,X1))),inverse(identity)),
    inference(forward_demodulation,[status(thm)],[f16,f126]) ).

fof(f146,plain,
    ! [X0] : multiply(identity,X0) = double_divide(double_divide(X0,identity),inverse(identity)),
    inference(paramodulation,[status(thm)],[f9,f118]) ).

fof(f157,plain,
    ! [X0] : multiply(identity,X0) = double_divide(inverse(X0),inverse(identity)),
    inference(forward_demodulation,[status(thm)],[f8,f146]) ).

fof(f212,plain,
    ! [X0,X1] : multiply(identity,double_divide(X0,X1)) = double_divide(multiply(X1,X0),inverse(identity)),
    inference(paramodulation,[status(thm)],[f14,f157]) ).

fof(f219,plain,
    ! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(multiply(X0,X1),inverse(identity)),
    inference(forward_demodulation,[status(thm)],[f15,f212]) ).

fof(f330,plain,
    ! [X0,X1] : double_divide(multiply(X0,double_divide(X1,identity)),inverse(X0)) = double_divide(double_divide(X1,identity),inverse(identity)),
    inference(paramodulation,[status(thm)],[f138,f115]) ).

fof(f347,plain,
    ! [X0,X1] : double_divide(multiply(X0,inverse(X1)),inverse(X0)) = double_divide(double_divide(X1,identity),inverse(identity)),
    inference(forward_demodulation,[status(thm)],[f8,f330]) ).

fof(f348,plain,
    ! [X0,X1] : double_divide(multiply(X0,inverse(X1)),inverse(X0)) = double_divide(inverse(X1),inverse(identity)),
    inference(forward_demodulation,[status(thm)],[f8,f347]) ).

fof(f349,plain,
    ! [X0,X1] : double_divide(multiply(X0,inverse(X1)),inverse(X0)) = multiply(identity,X1),
    inference(forward_demodulation,[status(thm)],[f157,f348]) ).

fof(f352,plain,
    ! [X0] : multiply(identity,X0) = inverse(multiply(identity,inverse(X0))),
    inference(paramodulation,[status(thm)],[f219,f349]) ).

fof(f371,plain,
    ! [X0] : multiply(identity,X0) = multiply(identity,inverse(inverse(X0))),
    inference(forward_demodulation,[status(thm)],[f17,f352]) ).

fof(f372,plain,
    ! [X0] : multiply(identity,X0) = multiply(identity,multiply(identity,X0)),
    inference(forward_demodulation,[status(thm)],[f16,f371]) ).

fof(f384,plain,
    ! [X0,X1] : multiply(identity,double_divide(X0,X1)) = multiply(identity,inverse(multiply(X1,X0))),
    inference(paramodulation,[status(thm)],[f15,f372]) ).

fof(f398,plain,
    ! [X0,X1] : inverse(multiply(X0,X1)) = multiply(identity,inverse(multiply(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f15,f384]) ).

fof(f770,plain,
    ! [X0] : inverse(identity) = double_divide(double_divide(X0,double_divide(multiply(identity,X0),inverse(identity))),inverse(identity)),
    inference(paramodulation,[status(thm)],[f157,f127]) ).

fof(f795,plain,
    inverse(identity) = identity,
    inference(forward_demodulation,[status(thm)],[f138,f770]) ).

fof(f1033,plain,
    ! [X0,X1] : X0 = double_divide(double_divide(X1,double_divide(double_divide(inverse(X1),X0),inverse(identity))),identity),
    inference(backward_demodulation,[status(thm)],[f795,f127]) ).

fof(f1042,plain,
    ! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,double_divide(identity,inverse(X0))),identity),
    inference(backward_demodulation,[status(thm)],[f795,f118]) ).

fof(f1048,plain,
    ! [X0] : identity = multiply(multiply(identity,X0),inverse(X0)),
    inference(backward_demodulation,[status(thm)],[f795,f30]) ).

fof(f1056,plain,
    multiply(identity,identity) = inverse(identity),
    inference(paramodulation,[status(thm)],[f795,f16]) ).

fof(f1058,plain,
    ! [X0,X1] : X0 = inverse(double_divide(X1,double_divide(double_divide(inverse(X1),X0),inverse(identity)))),
    inference(forward_demodulation,[status(thm)],[f8,f1033]) ).

fof(f1059,plain,
    ! [X0,X1] : X0 = multiply(double_divide(double_divide(inverse(X1),X0),inverse(identity)),X1),
    inference(forward_demodulation,[status(thm)],[f14,f1058]) ).

fof(f1060,plain,
    ! [X0,X1] : X0 = multiply(double_divide(double_divide(inverse(X1),X0),identity),X1),
    inference(forward_demodulation,[status(thm)],[f795,f1059]) ).

fof(f1061,plain,
    ! [X0,X1] : X0 = multiply(inverse(double_divide(inverse(X1),X0)),X1),
    inference(forward_demodulation,[status(thm)],[f8,f1060]) ).

fof(f1062,plain,
    ! [X0,X1] : X0 = multiply(multiply(X0,inverse(X1)),X1),
    inference(forward_demodulation,[status(thm)],[f14,f1061]) ).

fof(f1072,plain,
    ! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,double_divide(identity,inverse(X0)))),
    inference(forward_demodulation,[status(thm)],[f8,f1042]) ).

fof(f1073,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(double_divide(identity,inverse(X0)),X1),
    inference(forward_demodulation,[status(thm)],[f14,f1072]) ).

fof(f1080,plain,
    multiply(identity,identity) = identity,
    inference(forward_demodulation,[status(thm)],[f795,f1056]) ).

fof(f1159,plain,
    ! [X0,X1,X2,X3] : X0 = double_divide(double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),double_divide(double_divide(X3,X0),identity)),inverse(identity)),
    inference(forward_demodulation,[status(thm)],[f1080,f143]) ).

fof(f1160,plain,
    ! [X0,X1,X2,X3] : X0 = double_divide(double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),inverse(double_divide(X3,X0))),inverse(identity)),
    inference(forward_demodulation,[status(thm)],[f8,f1159]) ).

fof(f1161,plain,
    ! [X0,X1,X2,X3] : X0 = double_divide(double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),multiply(X0,X3)),inverse(identity)),
    inference(forward_demodulation,[status(thm)],[f14,f1160]) ).

fof(f1162,plain,
    ! [X0,X1,X2,X3] : X0 = double_divide(double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),multiply(X0,X3)),identity),
    inference(forward_demodulation,[status(thm)],[f795,f1161]) ).

fof(f1163,plain,
    ! [X0,X1,X2,X3] : X0 = inverse(double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),multiply(X0,X3))),
    inference(forward_demodulation,[status(thm)],[f8,f1162]) ).

fof(f1164,plain,
    ! [X0,X1,X2,X3] : X0 = multiply(multiply(X0,X1),double_divide(X2,double_divide(double_divide(double_divide(X2,X3),X1),inverse(X3)))),
    inference(forward_demodulation,[status(thm)],[f14,f1163]) ).

fof(f1186,plain,
    ! [X0,X1,X2,X3] : inverse(multiply(multiply(X0,X1),double_divide(X2,double_divide(double_divide(double_divide(X2,X3),X1),inverse(X3))))) = multiply(identity,inverse(X0)),
    inference(paramodulation,[status(thm)],[f1164,f398]) ).

fof(f1208,plain,
    ! [X0] : inverse(X0) = multiply(identity,inverse(X0)),
    inference(forward_demodulation,[status(thm)],[f1164,f1186]) ).

fof(f1226,plain,
    ! [X0] : inverse(multiply(identity,X0)) = inverse(X0),
    inference(backward_demodulation,[status(thm)],[f1208,f17]) ).

fof(f1279,plain,
    ! [X0,X1,X2] : double_divide(double_divide(double_divide(inverse(X0),X1),X2),inverse(X1)) = double_divide(double_divide(X0,X2),identity),
    inference(forward_demodulation,[status(thm)],[f795,f135]) ).

fof(f1280,plain,
    ! [X0,X1,X2] : double_divide(double_divide(double_divide(inverse(X0),X1),X2),inverse(X1)) = inverse(double_divide(X0,X2)),
    inference(forward_demodulation,[status(thm)],[f8,f1279]) ).

fof(f1281,plain,
    ! [X0,X1,X2] : double_divide(double_divide(double_divide(inverse(X0),X1),X2),inverse(X1)) = multiply(X2,X0),
    inference(forward_demodulation,[status(thm)],[f14,f1280]) ).

fof(f1319,plain,
    ! [X0,X1] : X0 = double_divide(double_divide(X1,double_divide(double_divide(identity,X0),multiply(identity,X1))),identity),
    inference(forward_demodulation,[status(thm)],[f795,f145]) ).

fof(f1320,plain,
    ! [X0,X1] : X0 = inverse(double_divide(X1,double_divide(double_divide(identity,X0),multiply(identity,X1)))),
    inference(forward_demodulation,[status(thm)],[f8,f1319]) ).

fof(f1321,plain,
    ! [X0,X1] : X0 = multiply(double_divide(double_divide(identity,X0),multiply(identity,X1)),X1),
    inference(forward_demodulation,[status(thm)],[f14,f1320]) ).

fof(f1392,plain,
    ! [X0] : multiply(identity,X0) = double_divide(identity,inverse(multiply(identity,X0))),
    inference(paramodulation,[status(thm)],[f1048,f349]) ).

fof(f1403,plain,
    ! [X0] : multiply(identity,X0) = double_divide(identity,inverse(X0)),
    inference(forward_demodulation,[status(thm)],[f1226,f1392]) ).

fof(f1511,plain,
    ! [X0] : multiply(identity,inverse(X0)) = double_divide(identity,multiply(identity,X0)),
    inference(paramodulation,[status(thm)],[f16,f1403]) ).

fof(f1524,plain,
    ! [X0] : inverse(X0) = double_divide(identity,multiply(identity,X0)),
    inference(forward_demodulation,[status(thm)],[f1208,f1511]) ).

fof(f1845,plain,
    ! [X0] : identity = multiply(X0,inverse(X0)),
    inference(backward_demodulation,[status(thm)],[f1846,f1048]) ).

fof(f1846,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(multiply(identity,X0),X1),
    inference(forward_demodulation,[status(thm)],[f1403,f1073]) ).

fof(f1900,plain,
    ! [X0] : X0 = multiply(identity,X0),
    inference(paramodulation,[status(thm)],[f1845,f1062]) ).

fof(f1934,plain,
    ! [X0] : inverse(X0) = double_divide(identity,X0),
    inference(backward_demodulation,[status(thm)],[f1900,f1524]) ).

fof(f1937,plain,
    ! [X0,X1] : X0 = multiply(double_divide(double_divide(identity,X0),X1),X1),
    inference(backward_demodulation,[status(thm)],[f1900,f1321]) ).

fof(f1939,plain,
    ! [X0] : identity = double_divide(inverse(X0),X0),
    inference(backward_demodulation,[status(thm)],[f1900,f25]) ).

fof(f1942,plain,
    ! [X0] : X0 = inverse(inverse(X0)),
    inference(backward_demodulation,[status(thm)],[f1900,f16]) ).

fof(f2001,plain,
    ! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(identity,X0),inverse(X1)),
    inference(paramodulation,[status(thm)],[f1939,f1281]) ).

fof(f2009,plain,
    ! [X0,X1] : multiply(X0,X1) = double_divide(inverse(X0),inverse(X1)),
    inference(forward_demodulation,[status(thm)],[f1934,f2001]) ).

fof(f2194,plain,
    ! [X0,X1] : X0 = multiply(double_divide(inverse(X0),X1),X1),
    inference(forward_demodulation,[status(thm)],[f1934,f1937]) ).

fof(f2200,plain,
    ! [X0,X1] : inverse(X0) = multiply(double_divide(X0,X1),X1),
    inference(paramodulation,[status(thm)],[f1942,f2194]) ).

fof(f2547,plain,
    ! [X0,X1,X2] : multiply(X0,X1) = double_divide(double_divide(multiply(X1,X2),X0),inverse(inverse(X2))),
    inference(paramodulation,[status(thm)],[f2009,f1281]) ).

fof(f2564,plain,
    ! [X0,X1,X2] : multiply(X0,X1) = double_divide(double_divide(multiply(X1,X2),X0),X2),
    inference(forward_demodulation,[status(thm)],[f1942,f2547]) ).

fof(f2915,plain,
    ! [X0,X1,X2] : inverse(double_divide(multiply(X0,X1),X2)) = multiply(multiply(X2,X0),X1),
    inference(paramodulation,[status(thm)],[f2564,f2200]) ).

fof(f2939,plain,
    ! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(multiply(X2,X0),X1),
    inference(forward_demodulation,[status(thm)],[f14,f2915]) ).

fof(f2940,plain,
    $false,
    inference(resolution,[status(thm)],[f2939,f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP486-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue Apr 30 00:17:36 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  % Drodi V3.6.0
% 0.20/0.47  % Refutation found
% 0.20/0.47  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.47  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.50  % Elapsed time: 0.140445 seconds
% 0.20/0.50  % CPU time: 1.032925 seconds
% 0.20/0.50  % Total memory used: 33.183 MB
% 0.20/0.50  % Net memory used: 30.978 MB
%------------------------------------------------------------------------------