TSTP Solution File: GRP080-1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP080-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 20:19:10 EDT 2024
% Result : Unsatisfiable 0.12s 0.43s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 8
% Syntax : Number of formulae : 110 ( 94 unt; 0 def)
% Number of atoms : 129 ( 106 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 16 ~; 16 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 162 ( 162 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = Z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = double_divide(double_divide(Y,X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : inverse(X) = double_divide(X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : identity = double_divide(X,inverse(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| 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(identity,double_divide(X0,double_divide(X1,identity))),double_divide(double_divide(X1,double_divide(X2,X0)),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(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f11,plain,
( spl0_0
<=> multiply(inverse(a1),a1) = identity ),
introduced(split_symbol_definition) ).
fof(f13,plain,
( multiply(inverse(a1),a1) != identity
| spl0_0 ),
inference(component_clause,[status(thm)],[f11]) ).
fof(f14,plain,
( spl0_1
<=> multiply(identity,a2) = a2 ),
introduced(split_symbol_definition) ).
fof(f16,plain,
( multiply(identity,a2) != a2
| spl0_1 ),
inference(component_clause,[status(thm)],[f14]) ).
fof(f17,plain,
( spl0_2
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(split_symbol_definition) ).
fof(f19,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(component_clause,[status(thm)],[f17]) ).
fof(f20,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f10,f11,f14,f17]) ).
fof(f21,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,double_divide(X1,identity))),multiply(double_divide(X2,X0),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f7,f6]) ).
fof(f22,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,inverse(X1))),multiply(double_divide(X2,X0),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f8,f21]) ).
fof(f23,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f25,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f23]) ).
fof(f26,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f23,f9]) ).
fof(f36,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f26,f22]) ).
fof(f37,plain,
! [X0,X1] : double_divide(double_divide(identity,identity),multiply(double_divide(X0,X1),X1)) = X0,
inference(paramodulation,[status(thm)],[f9,f22]) ).
fof(f38,plain,
! [X0,X1] : double_divide(inverse(identity),multiply(double_divide(X0,X1),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f37]) ).
fof(f39,plain,
! [X0,X1] : double_divide(identity,multiply(double_divide(X0,X1),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f36,f38]) ).
fof(f43,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(inverse(X0),inverse(X1))),multiply(identity,X1)) = X0,
inference(paramodulation,[status(thm)],[f9,f22]) ).
fof(f44,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),multiply(inverse(X1),X0)) = X1,
inference(paramodulation,[status(thm)],[f8,f22]) ).
fof(f47,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(X0,X1),X2),double_divide(identity,double_divide(X1,inverse(X2)))) = inverse(X0),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f57,plain,
! [X0] : double_divide(double_divide(identity,identity),multiply(inverse(X0),identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f44]) ).
fof(f58,plain,
! [X0] : double_divide(inverse(identity),multiply(inverse(X0),identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f57]) ).
fof(f59,plain,
! [X0] : double_divide(identity,multiply(inverse(X0),identity)) = X0,
inference(forward_demodulation,[status(thm)],[f36,f58]) ).
fof(f71,plain,
! [X0,X1] : double_divide(identity,multiply(multiply(X0,X1),identity)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f23,f59]) ).
fof(f99,plain,
! [X0] : multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(paramodulation,[status(thm)],[f25,f25]) ).
fof(f100,plain,
multiply(identity,identity) = inverse(identity),
inference(paramodulation,[status(thm)],[f36,f25]) ).
fof(f101,plain,
multiply(identity,identity) = identity,
inference(forward_demodulation,[status(thm)],[f36,f100]) ).
fof(f109,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,multiply(identity,X1))),multiply(double_divide(X2,X0),inverse(X1))) = X2,
inference(paramodulation,[status(thm)],[f25,f22]) ).
fof(f180,plain,
! [X0,X1,X2] : double_divide(identity,multiply(X0,multiply(double_divide(X0,X1),X2))) = double_divide(identity,double_divide(X1,inverse(X2))),
inference(paramodulation,[status(thm)],[f22,f39]) ).
fof(f181,plain,
! [X0,X1] : double_divide(identity,multiply(identity,multiply(X0,X1))) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f26,f39]) ).
fof(f182,plain,
! [X0] : double_divide(identity,multiply(identity,inverse(X0))) = X0,
inference(paramodulation,[status(thm)],[f9,f39]) ).
fof(f189,plain,
! [X0,X1] : multiply(multiply(double_divide(X0,X1),X1),identity) = inverse(X0),
inference(paramodulation,[status(thm)],[f39,f23]) ).
fof(f328,plain,
! [X0,X1] : multiply(multiply(identity,multiply(X0,X1)),identity) = inverse(double_divide(X1,X0)),
inference(paramodulation,[status(thm)],[f26,f189]) ).
fof(f329,plain,
! [X0,X1] : multiply(multiply(identity,multiply(X0,X1)),identity) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f23,f328]) ).
fof(f332,plain,
! [X0,X1] : double_divide(identity,inverse(X0)) = double_divide(X1,double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f189,f71]) ).
fof(f355,plain,
! [X0,X1] : double_divide(identity,multiply(identity,multiply(X0,X1))) = double_divide(identity,double_divide(multiply(identity,inverse(X0)),inverse(X1))),
inference(paramodulation,[status(thm)],[f182,f180]) ).
fof(f356,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(identity,double_divide(multiply(identity,inverse(X1)),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f181,f355]) ).
fof(f399,plain,
! [X0] : double_divide(multiply(identity,inverse(X0)),X0) = double_divide(identity,identity),
inference(paramodulation,[status(thm)],[f9,f356]) ).
fof(f400,plain,
! [X0] : double_divide(multiply(identity,inverse(X0)),X0) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f8,f399]) ).
fof(f401,plain,
! [X0] : double_divide(multiply(identity,inverse(X0)),X0) = identity,
inference(forward_demodulation,[status(thm)],[f36,f400]) ).
fof(f404,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,double_divide(multiply(identity,identity),inverse(X0))),
inference(paramodulation,[status(thm)],[f36,f356]) ).
fof(f405,plain,
! [X0] : inverse(X0) = double_divide(identity,double_divide(multiply(identity,identity),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f8,f404]) ).
fof(f406,plain,
! [X0] : inverse(X0) = double_divide(identity,double_divide(identity,inverse(X0))),
inference(forward_demodulation,[status(thm)],[f101,f405]) ).
fof(f410,plain,
! [X0] : double_divide(identity,X0) = double_divide(identity,double_divide(multiply(identity,inverse(X0)),identity)),
inference(paramodulation,[status(thm)],[f36,f356]) ).
fof(f411,plain,
! [X0] : double_divide(identity,X0) = double_divide(identity,inverse(multiply(identity,inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f332,f410]) ).
fof(f412,plain,
! [X0] : double_divide(identity,X0) = double_divide(identity,multiply(identity,inverse(inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f99,f411]) ).
fof(f413,plain,
! [X0] : double_divide(identity,X0) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f182,f412]) ).
fof(f469,plain,
! [X0] : inverse(multiply(inverse(X0),identity)) = X0,
inference(backward_demodulation,[status(thm)],[f413,f59]) ).
fof(f473,plain,
! [X0,X1] : double_divide(X0,X1) = inverse(double_divide(multiply(identity,inverse(X1)),inverse(X0))),
inference(backward_demodulation,[status(thm)],[f413,f356]) ).
fof(f474,plain,
! [X0,X1] : double_divide(X0,X1) = multiply(inverse(X0),multiply(identity,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f23,f473]) ).
fof(f477,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(X0,inverse(X1))),multiply(double_divide(X2,X0),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f413,f22]) ).
fof(f478,plain,
! [X0,X1,X2] : double_divide(multiply(inverse(X0),X1),multiply(double_divide(X2,X1),X0)) = X2,
inference(forward_demodulation,[status(thm)],[f23,f477]) ).
fof(f479,plain,
! [X0] : inverse(X0) = double_divide(identity,inverse(inverse(X0))),
inference(backward_demodulation,[status(thm)],[f413,f406]) ).
fof(f480,plain,
! [X0] : inverse(X0) = inverse(inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f413,f479]) ).
fof(f481,plain,
! [X0] : inverse(X0) = multiply(identity,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f25,f480]) ).
fof(f513,plain,
! [X0,X1] : double_divide(inverse(double_divide(inverse(X0),inverse(X1))),multiply(identity,X1)) = X0,
inference(backward_demodulation,[status(thm)],[f413,f43]) ).
fof(f514,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),inverse(X1)),multiply(identity,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f23,f513]) ).
fof(f554,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(X0,X1),X2),inverse(double_divide(X1,inverse(X2)))) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f413,f47]) ).
fof(f555,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(X0,X1),X2),multiply(inverse(X2),X1)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f23,f554]) ).
fof(f563,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(X0,multiply(identity,X1))),multiply(double_divide(X2,X0),inverse(X1))) = X2,
inference(backward_demodulation,[status(thm)],[f413,f109]) ).
fof(f564,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(identity,X0),X1),multiply(double_divide(X2,X1),inverse(X0))) = X2,
inference(forward_demodulation,[status(thm)],[f23,f563]) ).
fof(f573,plain,
! [X0,X1] : inverse(multiply(identity,multiply(X0,X1))) = double_divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f413,f181]) ).
fof(f574,plain,
! [X0,X1] : multiply(identity,inverse(multiply(X0,X1))) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f99,f573]) ).
fof(f575,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f481,f574]) ).
fof(f586,plain,
! [X0,X1] : double_divide(X0,X1) = multiply(inverse(X0),inverse(X1)),
inference(backward_demodulation,[status(thm)],[f481,f474]) ).
fof(f595,plain,
! [X0] : double_divide(inverse(X0),X0) = identity,
inference(backward_demodulation,[status(thm)],[f481,f401]) ).
fof(f599,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f575,f469]) ).
fof(f600,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f413,f599]) ).
fof(f601,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f25,f600]) ).
fof(f615,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),multiply(identity,X0)) = X1,
inference(backward_demodulation,[status(thm)],[f586,f514]) ).
fof(f616,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f601,f615]) ).
fof(f631,plain,
! [X0,X1] : multiply(multiply(X0,X1),identity) = multiply(X0,X1),
inference(backward_demodulation,[status(thm)],[f601,f329]) ).
fof(f635,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),multiply(double_divide(X2,X1),inverse(X0))) = X2,
inference(backward_demodulation,[status(thm)],[f601,f564]) ).
fof(f650,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f631,f189]) ).
fof(f690,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f616,f616]) ).
fof(f696,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f616,f23]) ).
fof(f738,plain,
! [X0] : double_divide(inverse(X0),identity) = X0,
inference(paramodulation,[status(thm)],[f9,f690]) ).
fof(f739,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f738]) ).
fof(f807,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),X1),multiply(identity,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f595,f478]) ).
fof(f808,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),X1),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f601,f807]) ).
fof(f937,plain,
! [X0,X1] : multiply(multiply(identity,X0),multiply(inverse(X0),X1)) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f595,f555]) ).
fof(f938,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = inverse(inverse(X1)),
inference(forward_demodulation,[status(thm)],[f601,f937]) ).
fof(f939,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f739,f938]) ).
fof(f996,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(inverse(X0),X1),
inference(paramodulation,[status(thm)],[f696,f939]) ).
fof(f1015,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),double_divide(inverse(double_divide(X2,X1)),X0)) = X2,
inference(backward_demodulation,[status(thm)],[f996,f635]) ).
fof(f1016,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),double_divide(multiply(X1,X2),X0)) = X2,
inference(forward_demodulation,[status(thm)],[f23,f1015]) ).
fof(f1087,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f808,f650]) ).
fof(f1088,plain,
! [X0,X1] : multiply(inverse(X0),X1) = double_divide(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f575,f1087]) ).
fof(f1323,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = inverse(double_divide(multiply(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1016,f696]) ).
fof(f1324,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f23,f1323]) ).
fof(f1333,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(backward_demodulation,[status(thm)],[f1324,f19]) ).
fof(f1334,plain,
( $false
| spl0_2 ),
inference(trivial_equality_resolution,[status(esa)],[f1333]) ).
fof(f1335,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f1334]) ).
fof(f1419,plain,
( double_divide(a1,inverse(a1)) != identity
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f1088,f13]) ).
fof(f1420,plain,
( identity != identity
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f9,f1419]) ).
fof(f1421,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f1420]) ).
fof(f1422,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f1421]) ).
fof(f1423,plain,
( a2 != a2
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f601,f16]) ).
fof(f1424,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f1423]) ).
fof(f1425,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f1424]) ).
fof(f1426,plain,
$false,
inference(sat_refutation,[status(thm)],[f20,f1335,f1422,f1425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP080-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35 % Computer : n007.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Apr 30 00:12:17 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Drodi V3.6.0
% 0.12/0.43 % Refutation found
% 0.12/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.45 % Elapsed time: 0.086327 seconds
% 0.19/0.45 % CPU time: 0.574635 seconds
% 0.19/0.45 % Total memory used: 54.894 MB
% 0.19/0.45 % Net memory used: 52.986 MB
%------------------------------------------------------------------------------