TSTP Solution File: GRP079-1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP079-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 104 ( 88 unt; 0 def)
% Number of atoms : 123 ( 100 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 16 ~; 16 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 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 : 173 ( 173 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : double_divide(double_divide(identity,X),double_divide(double_divide(double_divide(Y,Z),double_divide(identity,identity)),double_divide(X,Z))) = Y,
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,X0),double_divide(double_divide(double_divide(X1,X2),double_divide(identity,identity)),double_divide(X0,X2))) = X1,
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,X0),double_divide(double_divide(double_divide(X1,X2),inverse(identity)),double_divide(X0,X2))) = X1,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f22,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f24,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f22]) ).
fof(f25,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f22,f9]) ).
fof(f36,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(double_divide(double_divide(X0,X1),inverse(identity)),double_divide(identity,X1))) = X0,
inference(paramodulation,[status(thm)],[f8,f21]) ).
fof(f40,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(identity,inverse(identity)),double_divide(X0,inverse(X1)))) = X1,
inference(paramodulation,[status(thm)],[f9,f21]) ).
fof(f41,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(X0,inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f40]) ).
fof(f42,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(inverse(X1),inverse(identity)),double_divide(X0,identity))) = X1,
inference(paramodulation,[status(thm)],[f8,f21]) ).
fof(f43,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(inverse(X1),inverse(identity)),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X3),inverse(identity)),double_divide(X0,X3))),inverse(identity)),X2)) = X1,
inference(paramodulation,[status(thm)],[f21,f21]) ).
fof(f57,plain,
! [X0] : double_divide(inverse(identity),double_divide(identity,double_divide(identity,inverse(X0)))) = X0,
inference(paramodulation,[status(thm)],[f8,f41]) ).
fof(f58,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f41]) ).
fof(f59,plain,
! [X0] : double_divide(double_divide(identity,X0),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f58]) ).
fof(f66,plain,
double_divide(identity,inverse(identity)) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f59]) ).
fof(f67,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f9,f66]) ).
fof(f72,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(double_divide(X1,inverse(identity)),inverse(identity)),X0)) = X1,
inference(paramodulation,[status(thm)],[f59,f21]) ).
fof(f73,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(double_divide(X1,identity),inverse(identity)),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f67,f72]) ).
fof(f74,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(inverse(X1),inverse(identity)),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f73]) ).
fof(f75,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(inverse(X1),identity),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f67,f74]) ).
fof(f76,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(inverse(inverse(X1)),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f75]) ).
fof(f77,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(multiply(identity,X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f24,f76]) ).
fof(f78,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(X1,inverse(identity)),double_divide(X0,inverse(identity)))) = double_divide(identity,X1),
inference(paramodulation,[status(thm)],[f59,f21]) ).
fof(f79,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(X1,identity),double_divide(X0,inverse(identity)))) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f67,f78]) ).
fof(f80,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(inverse(X1),double_divide(X0,inverse(identity)))) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f8,f79]) ).
fof(f81,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(inverse(X1),double_divide(X0,identity))) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f67,f80]) ).
fof(f82,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(inverse(X1),inverse(X0))) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f8,f81]) ).
fof(f87,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = X0,
inference(backward_demodulation,[status(thm)],[f67,f59]) ).
fof(f88,plain,
! [X0] : inverse(double_divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f87]) ).
fof(f89,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f22,f88]) ).
fof(f100,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(identity,inverse(X0)))) = X0,
inference(backward_demodulation,[status(thm)],[f67,f57]) ).
fof(f107,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(double_divide(X1,double_divide(double_divide(double_divide(X2,X3),inverse(identity)),double_divide(X0,X3))),identity),X2)) = X1,
inference(backward_demodulation,[status(thm)],[f67,f44]) ).
fof(f108,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(inverse(double_divide(X1,double_divide(double_divide(double_divide(X2,X3),inverse(identity)),double_divide(X0,X3)))),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f107]) ).
fof(f109,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(multiply(double_divide(double_divide(double_divide(X1,X2),inverse(identity)),double_divide(X0,X2)),X3),X1)) = X3,
inference(forward_demodulation,[status(thm)],[f22,f108]) ).
fof(f110,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(multiply(double_divide(double_divide(double_divide(X1,X2),identity),double_divide(X0,X2)),X3),X1)) = X3,
inference(forward_demodulation,[status(thm)],[f67,f109]) ).
fof(f111,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(multiply(double_divide(inverse(double_divide(X1,X2)),double_divide(X0,X2)),X3),X1)) = X3,
inference(forward_demodulation,[status(thm)],[f8,f110]) ).
fof(f112,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(multiply(double_divide(multiply(X1,X2),double_divide(X0,X1)),X3),X2)) = X3,
inference(forward_demodulation,[status(thm)],[f22,f111]) ).
fof(f113,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(inverse(X1),identity),inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f67,f43]) ).
fof(f114,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(inverse(inverse(X1)),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f113]) ).
fof(f115,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f82,f114]) ).
fof(f121,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(double_divide(double_divide(X0,X1),identity),double_divide(identity,X1))) = X0,
inference(backward_demodulation,[status(thm)],[f67,f36]) ).
fof(f122,plain,
! [X0,X1] : double_divide(identity,double_divide(double_divide(double_divide(X0,X1),identity),double_divide(identity,X1))) = X0,
inference(forward_demodulation,[status(thm)],[f67,f121]) ).
fof(f123,plain,
! [X0,X1] : double_divide(identity,double_divide(inverse(double_divide(X0,X1)),double_divide(identity,X1))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f122]) ).
fof(f124,plain,
! [X0,X1] : double_divide(identity,double_divide(multiply(X0,X1),double_divide(identity,X0))) = X1,
inference(forward_demodulation,[status(thm)],[f22,f123]) ).
fof(f132,plain,
! [X0] : double_divide(identity,double_divide(identity,X0)) = X0,
inference(backward_demodulation,[status(thm)],[f115,f100]) ).
fof(f133,plain,
! [X0,X1,X2,X3] : double_divide(X0,double_divide(multiply(double_divide(multiply(X1,X2),double_divide(X0,X1)),X3),X2)) = X3,
inference(backward_demodulation,[status(thm)],[f132,f112]) ).
fof(f135,plain,
! [X0,X1] : double_divide(X0,double_divide(multiply(identity,X1),X0)) = X1,
inference(backward_demodulation,[status(thm)],[f132,f77]) ).
fof(f140,plain,
! [X0] : identity = double_divide(double_divide(identity,X0),X0),
inference(paramodulation,[status(thm)],[f89,f25]) ).
fof(f143,plain,
! [X0,X1] : double_divide(identity,multiply(X0,X1)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f22,f115]) ).
fof(f151,plain,
! [X0] : double_divide(identity,X0) = inverse(X0),
inference(paramodulation,[status(thm)],[f115,f132]) ).
fof(f165,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f151,f115]) ).
fof(f166,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f24,f165]) ).
fof(f172,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f151,f143]) ).
fof(f175,plain,
! [X0,X1] : inverse(double_divide(multiply(X0,X1),double_divide(identity,X0))) = X1,
inference(backward_demodulation,[status(thm)],[f151,f124]) ).
fof(f176,plain,
! [X0,X1] : multiply(double_divide(identity,X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f22,f175]) ).
fof(f177,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f151,f176]) ).
fof(f193,plain,
! [X0] : identity = double_divide(inverse(X0),X0),
inference(backward_demodulation,[status(thm)],[f151,f140]) ).
fof(f205,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(backward_demodulation,[status(thm)],[f166,f135]) ).
fof(f218,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f151,f22]) ).
fof(f219,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f89,f218]) ).
fof(f282,plain,
! [X0,X1,X2] : double_divide(inverse(X0),double_divide(multiply(double_divide(multiply(X0,X1),identity),X2),X1)) = X2,
inference(paramodulation,[status(thm)],[f193,f133]) ).
fof(f283,plain,
! [X0,X1,X2] : double_divide(inverse(X0),double_divide(multiply(inverse(multiply(X0,X1)),X2),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f8,f282]) ).
fof(f284,plain,
! [X0,X1,X2] : double_divide(inverse(X0),double_divide(multiply(double_divide(X1,X0),X2),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f172,f283]) ).
fof(f316,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f205,f205]) ).
fof(f328,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f205,f22]) ).
fof(f373,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f316,f22]) ).
fof(f416,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f219,f177]) ).
fof(f419,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),multiply(double_divide(X1,X0),X2)) = X2,
inference(paramodulation,[status(thm)],[f22,f177]) ).
fof(f471,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(inverse(X0),X1),
inference(paramodulation,[status(thm)],[f373,f416]) ).
fof(f482,plain,
! [X0,X1] : inverse(X0) = double_divide(multiply(inverse(X1),X0),X1),
inference(paramodulation,[status(thm)],[f416,f172]) ).
fof(f500,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = double_divide(inverse(X0),double_divide(X2,X1)),
inference(paramodulation,[status(thm)],[f22,f471]) ).
fof(f514,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,multiply(double_divide(X1,X0),X2))) = X2,
inference(backward_demodulation,[status(thm)],[f500,f284]) ).
fof(f544,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f482,f328]) ).
fof(f545,plain,
! [X0,X1] : multiply(inverse(X0),X1) = double_divide(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f172,f544]) ).
fof(f670,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = multiply(X3,multiply(double_divide(X3,double_divide(X1,X0)),X2)),
inference(paramodulation,[status(thm)],[f514,f514]) ).
fof(f707,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),X2) = multiply(X3,multiply(double_divide(X3,double_divide(X1,X0)),X2)),
inference(paramodulation,[status(thm)],[f514,f419]) ).
fof(f708,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f670,f707]) ).
fof(f718,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(backward_demodulation,[status(thm)],[f708,f19]) ).
fof(f719,plain,
( $false
| spl0_2 ),
inference(trivial_equality_resolution,[status(esa)],[f718]) ).
fof(f720,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f719]) ).
fof(f734,plain,
( double_divide(a1,inverse(a1)) != identity
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f545,f13]) ).
fof(f735,plain,
( identity != identity
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f9,f734]) ).
fof(f736,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f735]) ).
fof(f737,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f736]) ).
fof(f738,plain,
( a2 != a2
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f166,f16]) ).
fof(f739,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f738]) ).
fof(f740,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f739]) ).
fof(f741,plain,
$false,
inference(sat_refutation,[status(thm)],[f20,f720,f737,f740]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP079-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n019.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 00:21:44 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38 % Elapsed time: 0.039070 seconds
% 0.13/0.38 % CPU time: 0.206675 seconds
% 0.13/0.38 % Total memory used: 31.206 MB
% 0.13/0.38 % Net memory used: 30.733 MB
%------------------------------------------------------------------------------